Hmmh. Why ActivityPub? I mean I suppose it's alright as a standard for some turn based or slow trading game. But it's neither very efficient nor suited for realtime. And having long (and descriptive) JSON messages, queues, ... is baked in per design.
And it's not even interesting to a Mastodon user if player x sold y latinum to player z. So for lots of game logic we don't need messages in a common format that's federated to Mastodon, Lemmy, Peertube etc.
I think a nice and not too complicated coding challenge would be to design a world that spans multiple servers. Players could roam a world, go through some door or portal and the client seamlessly connects to the next server. So that part of the world (the other server instance) is behind that portal. That'd make sense from an in-game perspective and won't be that hard to implement. Basically it's just like any other game, just that the client auto-connects to servers with some internal logic and not just in the start menu. And ideally authentication would be federated. The new server could ask the player's home instance to authenticate them on entering the new instance.