Depends on what an "online game" is, if it's a casino, bitcoin gambling website and hence game, Yes. There are plenty of sites accepting and taking BTC, just check the gambling forum for them.

if you mean a skill-based game, there are few. Not chess of course but some games pop-up once in a while, difficult to last since computers would play better than humans most of the time.

if you mean a free game giving BTC, There was coinhopper and minesweeper before, not seeing many right now, but there should be one or two still running.