Someone correct me if I'm wrong but I think I read this somewhere. .io is an internet domain. Agar.io was the first of these games I believe and the creator picked .io instead of .com because it was easier to get the domain name he wanted. It was probably cheaper too. After that, the copycats used .io just to capitalize on Agar.io's success.
It's the top level domain for British Indian Ocean territory, but it's become fashionable for games now: https://en.wikipedia.org/wiki/.io#Popularity_in_recent_years
Appstore had an article for this. Agar.io started it, and it was supposed to be just some URL which linked to the game or something like that. The .io stuck when they added the game into the appstore. Kinda disappointing as to how there was really no special reasoning they came up with the ".io" in the game title considering it was copied by other games. LOL
Ahhh. I'd been wondering about this, myself. But, almost all definitions I've found didn't have anything to do with games.