I will start of with the clarification that "smokeless" powder which was used by the vast majority of the guns and cartridges of the war is not truly smokeless. While it does not put out the large black clouds that you see from firearms such as muskets, it does still have some smoke produced at the end of the barrel. This is pretty firearm and powder dependant though so some guns it's more noticeable than others.

I would also like to make note that the true nature of the footage is not known. Personally, I think its a little too close to the actual fighting for a cameraman to just standing there watching the action. It very well could be footage of a military exercise in which, obviously, real ammunition would not be used.

However, to actually answer your question of was black powder firearms used during WW1. The answer is yes, kind of. World War One introduced warfare on a massive scale with armies swelling to enormous sizes. Virtually every nation struggled with supplying these massive forces, some more than others. Over the course of the war, rifles would be damaged, lost, or destroyed in combat, sometimes faster than they could be replaced. This often meant that nations had to resort to using older firearms from their surplus caches or importing them to supplement the loss of equipment. A thing to note is that smokeless powder was introduced on a large scale in European militaries in the 1880s with the French invention of Poudre B in 1884 and the design and adoption of the first smokeless powder rifle, the Fusil Modèle 1886 "Lebel" in 1886 by the French. With the war beginning in 1914, its not a huge gap in time.

However, European nations all went into World War One fielding their own smokeless powder rifles. Most of these rifles were only 1 or 2 design generations away from their blackpowder ancestors. The French fielded the Lebel and Berthiers, only 1 and 2 designs away from black powder respectively. The Germans only 2 designs removed. The Russians as well as the British only 1 design. By the time of the war, black powder was not far removed technology wise so many still had many black powder rifles stashed away for surplus.

Now is the important part, most of these did not see front line use. The vast majority of black powder rifles that were issued back into service were given to logistics companies, transportation guards, or colonial troops. Giving these guns to men such as train station guards ensured they still had a weapons should they need it, but it freed up a more modern rifle to go the the front. It was better to give the truck driver the old Mauser 71/84 because he probably wasn't going to use it anyways, and it freed up the Gewehr 98 to go to a soldier on the frontline.

Many nations gave these inferior weapons to colonial troops as well. One reason as stated above, was the belief they wouldn't be in combat a ton as they were mostly defending the colonies and it freed up more modern equipment. A secondary reason for many nations to give colonial troops black powder was many nations feared giving troops raised in the colonies too modern of weapons. It was inherent fear of arming the native populations of their colonies and that one day they might use the weapons on them in an uprising or rebellion. Their view was giving them older weapons would eliminate some of the risk or difficulties if this was to happen.

There is one nation that field black powder rifles to a larger extend than other nations, that being Russia. Russia had extremely hard times supplying their armies at some point, relying on their old Berdan II rifles to help augment their losses of their 1891 Mosin Nagants. Russia also imported a lot of firearms from other nations such as France and the US. Most of these would be older obsolete rifles such as the French Gras rifle, a rifle from 1874. Some black powder rifles such as the French Gras and the Italian Vetterli's were updated to accept new smokeless powders with upgrades during the war, but many also still remained in black powder configurations. Other smaller nations such as Greece also used imported black powder rifles, even using them in WW2.

So to sum up, yes black powder rifles were used in WW1 but really only in limited capacities. Most nations only utilized them to give to troops in non-combat or rear positions in order to free up more rifles to go to the front. Russia really remained the only nation that fielded black powder rifles in any real measurable way on the front line. There are instances of some being used by other nations but it was not super common.