Obviously this was the debut of a lot of technologies that really ended up flourishing in the Second World War, but my question is whether or not they really played a decisive role in the end of the first one.
It's difficult to say.
Armored cars were a fine idea, but not meaningfully deployed in the sort of numbers necessary to make a huge impact. The most popular British model, for example (the Rolls Royce), only saw the production of 120 units in total over the course of the war, and these mostly ended up getting converted into transport or shipped to the Middle Eastern theatre. They proved essentially useless on the Western Front after the mobile opening stages of the war.
Tanks are another matter.
The initial idea for the tanks seems to have come from Major-General Sir Ernest Swinton, who in October of 1914 first proposed:
a power-driven, bullet-proof, armed engine, capable of destroying machine guns, of crossing country and trenches, of breaking through entanglements, and of climbing earthworks.
This amazing weapon was duly designed, and the first "tanks" (so-named to convince any unscrupulous observers watching their parts being shipped that they were merely new water tanks) made their limited debut at Flers on September 15, 1916, where they met with mixed success.
Their "influence" is somewhat difficult to measure given the limitations involved in producing and deploying them in the first place. On the one hand we are confronted with the tremendous enthusiasm of pretty much everyone involved, with certain notable theorists, statesmen and generals of the time almost convinced that the tank could win the war alone; on the other hand we are confronted with the construction problems, design flaws and environmental factors that plagued them from the first moment of their existence, and in the end must acknowledge that they were very far from living up to what had been expected of them.
We hear a lot about how "the generals" (that monolith!) resisted new technology out of some hidebound lack of imagination or fear that it wasn't somehow "proper." This is a greatly exaggerated thing to begin with, but in terms of tanks it's very far from the truth indeed. There was less reluctance about introducing the new weapon than there was regret that they could not introduce more of them and confusion over how to introduce them at all. They were damnably expensive to produce, slow to build, difficult to transport, and dramatically diminished in their power once the initial shock at their appearance had worn off. Still, many of their early proponents were almost fanatics on the subject; Winston Churchill, for example, in his capacity as Minister of Munitions in 1918, drafted a wildly hypothetical plan of attack that called for 10,000 tanks backed by an additional 8,000 to 10,000 tracked support vehicles (precursors to the APCs of the second war). This is a fantastic idea, or to be more precise fantastical; it ignores (as Churchill should have known then, but as he continued to ignore in his memoirs of the war published in the 1920s and 30s) the fact that no such manufacturing capacity existed, anywhere, to produce this number of tanks on the kind of timeframe that was envisioned.
We might look also to the ideas of Major General J.F.C. Fuller, who in the Spring of 1918 was inspired by the sight of British troops retreating near Peronne to imagine a future in which the tank made such a thing unnecessary. His idea ultimately became known as "Plan 1919", and we can find a fine description of its potential in A.J. Trythall's biography of Fuller:
[The basic concept] was derived from the question, 'Why were our troops retreating?' and the answer 'Because our command was paralysed.' The concept was 'strategic paralysis', to be brought about by attacking and cutting off the enemy's brains, in other words his field headquarters, from his fighting troops. 'Plan 1919' was originally called 'The Tactics of the Medium D Tank', but before becoming 'Plan 1919' became 'Strategical Paralysis as the Object of the Attack'. According to Fuller himself the idea was 'a psycho-tactical one', but he used 'strategical' rather than 'tactical' in conjunction with 'paralysis' because 'the primary aim of the attack was to paralyse the enemy's command and not his fighting forces... that is his strategical brain and not his fighting body.'
Fuller had based this plan on the imminent production of a then-still-hypothetical piece of weaponry, the Medium D tank. A single experimental model had been built in 1918 -- that was it. On paper it was absolutely wonderful by comparison to the rest of the tanks then available, but it only really existed on paper to begin with. This didn't stop Fuller from drafting a plan that would require 1,600 of the things, however, and an additional 400 smaller support tanks -- a plan that the course of events rendered moot, anyway, given that the war ended without it.
Those commanders who were able to make use of the tanks while the war was still in progress sent in similarly enormous purchase orders; Sir Douglas Haig, for example, had been absolutely convinced of the tank's importance even five months before any of them even arrived for his inspection, and only four days after their first action would place an order for another 1,000, to be delivered as quickly as possible.
The realities were almost dismal by comparison. There were 49 tanks available for their initial debut at Flers; only 32 of these actually reached the Front, with the rest being sidelined by a variety of mechanical and environmental problems. Further problems at the Front itself prevented all but 25 of the new vehicles from being deployed, and only 9 actually even made it to the German lines -- not an explosive start.
Still, they were an arguable success in their debut -- if we may call demonstrating dramatic potential without achieving much of it a success -- and one would think that Haig's enthusiastic request for a thousand of them would lead to increased production... but one would be wrong. By the opening of the Arras offensive six months later, only 60 were actually on hand, most of them actually having been refurbished from the action at Flers! By the height of Third Ypres this had only increased to 136. The opening of 1917 had seen the office initially in charge of tank production (the Heavy Branch of the Machine Gun Corps) make plans to produce 1,460 new tanks in the first nine months, including 1,000 of the Mark IVs and even, later in the year, some of the new Mark Vs. None of the latter ever did get produced that year, and of the former only 378 ever made it to the Battle of Cambrai in November -- where they were admittedly used to great effect.
None of this was made any easier by inter-departmental competition and basic design oversights, either. The Admiralty had been keeping a stranglehold on the supply of steel plate necessary for mass production of the tanks, and it was discovered belatedly that highly anticipated Mark IVs were being defeated in the field by the simple expedient of the Germans widening their trenches by two or three feet. This had been anticipated by the officers staffing the Tank HQ near the front lines, but none of the early recommendations they had made about improving the Mark IV's design had actually been accepted by its manufacturers, who felt they knew better.
The war's closing stages during the Battle of Amiens saw the deployment of a comparatively large number of tanks -- 342 Mark Vs and 72 Whippets. While they proved a potent force indeed, it would be worth considering their casualty rates:
Clearly there were still problems to be solved.
The main one was speed. Considerably behind the cavalry, armored cars and motorcycles of the time, the top speed of the 1918 Mark V on a smooth, open road was only 4.6 miles per hour. The same speed for the Medium Mark A Whippet was a more promising 8.3 miles per hour -- but, again, on a clear open road. Across the sort of crater-strewn, uneven terrain in which they would actually be deployed their usual speed was closer to 1-1.5 miles per hour -- hardly a replacement for cavalry when it came to swift maneuvers and immediate exploitation. They were also very poor as troop carriers; the great lumbering machines had serious ventilation problems that routinely left those riding in them in a state of near collapse after any sustained amount of time -- certainly in no condition for quick and dynamic action.
Worse still was the fact that, in spite of having been designed to repel small arms fire with impunity and traverse a variety of difficult terrains, there were still so many things that could just turn them into expensive wrecks at the drop of a hat. The things basically destroyed themselves; they were forever getting stuck in shell craters, or falling into trenches, or getting flipped over coming up or down hills, or simply breaking down in the middle of No Man's Land, stranding their crew in a very dangerous position indeed. Their armor was only barely "bullet-proof", and was in most cases wholly incapable of stopping the armor-piercing rounds developed to deal with them. Artillery was even worse; the gigantic, ponderous objects made amazing targets for gunners, and it was rare that more than a single well-aimed shell was needed to destroy one.
Sometimes this was taken to absurd extremes: the only German officer to have received the distinction of being mentioned in dispatches by Field Marshal Haig was the one who managed, while serving his gun single-handedly, to destroy sixteen British tanks one after another, each with a single shot. Haig notes this with a tone of frank admiration that was shared even by those on the scene, and it was a matter of some regret that the dedicated officer was finally killed at his gun.
Sorry for the digression -- in the end, I would have to offer my opinion that the influence of the tanks on the outcome of the war was more psychological than tactical or strategic, and that it would take until the second war for this particular type of weapon to really come into its own. I listed the numbers of tanks available to the British during the Last Hundred Days above -- the low three figures. During the German invasion of France in 1940, by comparison, the two combatant powers deployed almost 6,000 tanks between them.
Still, this is just my own take on it -- others are certainly possible.
Armoured warfare wasn't decisive in ending WWI. It played a role, sure, but it wasn't quite as influential as is often assumed. Tanks came onto the battlefield in 1915 and it should tell you something that the war continued until 1918.
Of course, at first tanks were very shoddy, often breaking down and barely being able to make their way across no-man's land. Many were just slowly driving coffins. They were lightly armoured, prone to mechanical failure and fires, lightly armed. More importantly, they weren't really integrated into the battle plan at first, mainly serving as mobile support for infantry.
This didn't last. The tanks improved and became integrated in the battle plan from give or take 1917 onwards. They definitely became more effective, no longer having to rely purely on the fact that giant, lumbering metal machines lurching towards the enemy lines tended to scare those enemies. One of the battles that's named as one of the earlier examples of the value of armoured warfare is the Battle of Cambrai. The tanks definitely performed well, yet still the battle was not won - the Germans retook most of the gained ground.
Finally, you have the Battle of Amiens, 'the black day of the German Army', where tanks were again present and were credited with basically helping win the battle that would end the years of trench warfare - and eventually the war. The thing is, and this is my main thesis here, that it wasn't so much the tanks, but the general advance in strategies and tactics, as well as some large scale evolutions which mean that the war was basically won even before this battle. At that point, it was just a matter of time before the Allies broke through the German lines. On the macro scale, the arrival of the Americans and the failure of the Spring Offensive were much more decisive than just the addition of tanks.
But closer to the ground then, my point is that a great deal of tactical and strategic evolutions finally came together and reached a point where they couldn't be resisted. I've sketched this evolution in this post. The earlier tanks weren't used effectively and along with other ineffective tactics, you'd have results such as the Somme. Later on, you had more thought-out and effective tactics, like those used at Cambrai. However, they eventually failed because the rest of the plan wasn't there yet and because the macro events I mentioned hadn't impacted the ability of the German army to respond yet.
Then finally, it was at Amiens that everything came together. Combined arms warfare, things like the creeping barrage, infiltration and stormtrooper tactics, the level of training and preparation of the troops, etc - all these things came together to form a whole that couldn't just win a skirmish, but could win a battle and actually build upon that victory.
So, long story short, the advances in armoured warfare certainly played a part in the final victory, but they themselves were just a part in the larger evolutions at play. An apt comparison would be the use of gas, which while devastating at first, quickly lost its importance and potency once the shock effect was gone. Gas was never influential in ending the war, because even when it was used successfully, the rest of the picture was incomplete and the armies couldn't capitalise on the success.
And, to emphasise, the advances in tank warfare - or even the general advances in tactics - wouldn't have even mattered if the events on the larger scale hadn't taken place.