The UK in 1914 was a world power having bases and territory directly and indirectly under its control on every continent.

Germany also had land (though much smaller then the UK) on several continents.

There where battles that took place outside of the trenches and the middle east. For example the Siege of Tsingtao was in the Pacific while the Battle of Coronel was in South America.

Thus we can see Battles taking place in South America, Africa, China, Europe, and the Middle East. By any definition that is world wide combat.

However it is also considered a world war because it involved thanks to Empire every continent and almost all the major power of the day. The US, Russia, Germany, France, UK, Italy, and Japan where all involved.

The majority of the fighting took place in Europe (the Western and Eastern fronts, Italy, the Balkans, Gallipoli), but non-European Ottoman territory saw plenty of combat, too (Egypt/Palestine, Arabia, Mesopotamia, the Caucasus). The naval war stretched around the world, with German commerce raiders active in the Pacific and Indian oceans early in the war, and major battles at Coronel and the Falkland Islands. On land, the German colonies saw varying degrees of conflict: most of Germany's colonies fell very quickly, but Paul von Lettow-Vorbeck led a successful guerilla campaign in German East Africa which lasted until the end of the war.

Still, most of the fighting was in Europe. But there's another reason to call WWI a World war--belligerents from all over the world participated. Tens of thousands of soldiers from the British Commonwealth, as well as the British and French colonial empires, fought in Europe and elsewhere. Other belligerents included Japan, the United States, and a long list of others.

Really, I think the question to ask is whether the First World War actually deserves the title of First.

The term 'world war' only entered English, most likely from the German term 'Weltkrieg', which means world war, a handful of years before the First World War. Contrary to what the term would lead you to think it didn't mean a war fought across the globe. According to the Oxford English Dictionary the definition of world war was a war involving the world's major nations. Under that definition it was obviously a world war as the world's major nations were involved.

/u/winterking07 touched on this a little bit, but there was significant fighting in Africa. German Southwest Africa (Namibia) was invaded by the British, which was initially repulsed before finally succeeding. In German East Africa Paul Von Lettow Vorbeck beat the British at Tanga and then ran circles around an invading South African Army.

The Japanese attacked Germany's colonies in the Pacific and occupied them. The other instances have been touched on by the other posters.

However, there's another reason that I haven't seen why WWI is a global war. Even if most parts of the world didn't see fighting, the vast majority of the world was mobilized for war production, and sent millions of men to fight in Europe. This was because to have the resources to fight such a massive conflict all the major powers had to lean on their Empires, which gave the entire world at least some stake in the conflict.

The First World War Episode Two: Global War, has a great overview of this. Also, chapter two or three of Peter Hart's "The Great War" has a great overview of the naval warfare in a global context.