If you mean that players are going to use computer power while playing a game to mine bitcoin, they'd earn so very very little bitcoin that they'd earn far more by collecting bottles.
It'd definitely be more rewarding to use crypto to pay for items, as well as using blockchain to track inventory and items. This is already in works I think by various projects aiming to achieve just that.
I don't know who Bitcoin's strongest ally will be, but it's not going to be people playing games on their computers.
The crypto market is growing almost exponentially, and more and more projects and companies are launching and adopting crypto/btc in various ways.
I remember Digibyte were supposed to have some Minecraft server you could turn diamonds into DGB or something like that, seems like that project died.
Either way, we surely have an interesting future for crypto as it becomes more adopted and used in everyday products and as payment methods.
Perhaps, a new type of crypto could be launched, which games could somehow integrate with, where ingame actions result in this crypto, and also it'd be the only way to acquire it..
not so much for monetary gain, more as some type of intertwined gaming-payment-platform where you can sell items from one game and buy stuff in another game.
That could be cool. Although the companies launching the games wouldn't earn from that, unless they're taking some fee from each transaction.