There were certain wars fought on the global scale before the 20th century which could be described as a world war. The Seven Years War is one of the first good example of this, in which Britain/Prussia and France/Russia/Austria fought in Theaters as disparate as Silesia in Eastern Europe to Fort Louisburg in Nova Scotia to the island of Martinique in the Caribbean to Senegal in Africa to Bengal in eastern India. The end of the war brought territorial changes as dramatic as that of the Great War in many areas: such as the acquisition of Quebec by the British and the ousting of the French from India. It is for those reasons that Winston Churchill called the seven years war the First World War.

The problem here is that we're pointing at the phrase "World War" as if it means something. The short answer is that the phrase "World War" basically didn't exist prior to the 1800s . The OED doesn't have a usage of the phrase in English until 1909.

To that end, it's difficult to have described any of the numerous large scale conflicts prior to the 20th century as a "world war" given that the phrase simply didn't exist... but those wars were every bit as global as WWI -- many moreso.

The only caveat I would make to that statement is that, while wars prior to WWI certainly took place in theatres of conflict as if not more diverse than those in WWI, in no war prior to WWI was a global supply chain as critical an aspect of the war as we saw in WWI.

By virtue of its status as the first truly protracted industrial war, the first world war became a conflict not just about armies and navies but about the complex flow of raw materials and manufactured goods without which the continuation of hostilities was impossible. To that end, one might plausibly claim that the war took place not just where fighting occurred but in every locale and transit lane that might supply the belligerents with the goods needed to continue the fight.

There were what can reasonably be described as global wars going back to the late 15th century, as soon as technology and transport made them possible. Karen Rasler and William Thompson have used the records of these wars to help construct long cycle theory, although they only explain the five periods of global war (treating WWI and WWII as a single period of global war) that occurred at the end/beginning of each century. They have lots of publications, but one that is easy to access and introduces the theory and the wars is available here. I'm a little leery of their historical approach, but the idea that European conflicts became global conflicts over time as European colonial control increased seems sound.