There were land battles on three continents: Europe, Asia, and Africa. The fighting in Africa and Asia included major powers (e.g., Britain and Dominions vs Germany, Britain vs Ottoman Empire, Russia vs Ottoman Empire, Japan vs Germany). There were naval battles in the Atlantic, the Pacific, and the Indian oceans.

Combatants from outside Europe and the British Empire included the USA, Brazil, Japan, China, and Thailand. The British Empire included Australia, Canada, India, New Zealand and South Africa.

Therefore, while the focus of the war was Europe, there were many battles outside Europe, and many combatants outside Europe.

Perhaps a more interesting question is why WWI isn't the "second world war"? The Seven Years' War (1756-1763) included fighting in North America, South America, India, and Africa as well as Europe. While the main combatants were European, other Asian and American states participated, and the fighting was more globally spread than the fighting in WWI.

To answer my own question, the Seven Years' War was long before WWI, 160 years earlier, and was no longer in living memory. WWI, on the other hand, was recent, and WWII could easily be viewed as "WWI round 2" (if we Eurocentrically ignore the Second Sino-Japanese War).