I'm not going to try to predict what history will look like 80 years from now, or whether 9/11 or covid will be considered more significant by then, but this does raise an interesting question of how people in 1913 perceived the nascent 20th century.
Obviously things happened over those 13 years, but whatever they were, history ultimately decided that they were inconsequential enough for the "20th-century events" Wikipedia article to not even mention anything before WWI: https://en.wikipedia.org/wiki/20th-century_events
WWII isn't really a single war as much as it is a collection of several wars, be they wars of territorial expansion (e.g., Germany, USSR), ideological civil war (e.g., China), non-ideological civil war (e.g., France), or random local conflicts (e.g., Yugoslav coup) which are all occurring in the context of one another. In many places, it's often a three-way war, with all parties equally at odds with one another, instead of the simple Axis v. Allies it's usually presented as. Start including the full context of these conflicts into the timeframe of WWII, and you push its start date back arguably to 1931, only 8 years after the last cleanup war of WWI (the Russian Civil War).
Viewed from an international relations perspective, combining WWI and WWII into a single period of flux makes sense. WWI makes the death of great power influence, but the attempted resolution afterwards (League of Nations) was impotent and unable to have any major effect on the international crises that arose, unlike the great power conferences preceding WWI. Instead, the end of WWII ushers in the era of superpower relations, where essentially the USA and USSR drive international relations for the rest of the world.
Did WWI define the 20th century, or was it WWII? I think WWI demarcates the 1st of a series of really big, interrelated events. I suspect Covid-19 could be the 1st of a series of really big, interrelated events.