Accepting the global-anarchy/ATR premise (which is itself a game), I'd say it depends where the emphasis in that sentence lies. Would there be games (like, for example, the world cup or the olympic games)? Absolutely, and arguably more, but we might also expect that our current approach to entertainment and play as a cathartic opposite to work would dissolve--in other words, there is something about our common situation that makes us imagine these games as games, when in the real event that framework might not fit.
Would there be games that are very much like the world cup/olympics? Certainly not, since nationalism and capitalism make up most of what defines those games.
Would there be games that, like the world cup/olympics, take place at an international scale? It's a fine idea, but they would probably be very slow, because I don't think international communications and transporatation infrastructure would function as it does now. And they would be more about the experience and its retelling, and less about spectation.
PS - If you want a less-ATR and more 'today' answer, a lot of world cup and olympics have been resisted by anarchists. There are texts, zines, propaganda, demo report-backs, etc that talk a lot about why resist these events. But I imagine that's not what you're looking for?