If I recall correctly, there is in the past but small projects like the Flappy Bird game called Flappy Coin (if I got the name right) and those small games in Micro Earnings. Basically just like a faucet but not the usual ones. There are also some projects who held ICOs which related to games but I doubt some of them got successful.

If you are talking about MMORPG, RPG, First Shooter, MOBA, browser-based games, etc. I doubt there is today.

Or just head to gambling section, where you can see a literal crypto online game.