If you’re talking about self-hosted game servers, those already exists (see Minecraft), but it depends on whether they allow it or not. Reversing is possible, yeah, but it would take stupid amount of effort without their cooperation.
Main challenge of federated in the sense that there are communications between servers as well as client and server is probably going to be latency. If I were building something like this, I would rather have a protocol that redirects you to the actual game server so that you have direct connection to it rather than having your home instance acting as a proxy to the remote instance. Your home server would simply tell the remote server that your account is legitimate. This would be one of those “cracked” Minecraft server except they rely on an external server for account verification.
A program that covers all kinds of games is going to be challenging due to sheer variety there would be. You could build a specialised protocol for a specific genre of games, but I think at that point, it would make more sense to build your own game, and use Fediverse identity to identify the user.