You can't build something like that directly on Hive. Think of Hive as a big decentralised storage. You can put all kinds of data on there, but in order to use it, you'll need to create applications which read from and write to the data.
In order for the user to be "online", you'll need to utilise real-time frameworks (i.e. https://colyseus.io/ - which I'm using for both Ethgard & Ethgard Legends). When the user changes maps, opens chest or defeats a monster, you could update the data onchain, but you will always need an offchain application layer between Hive and the user.
Yeah I have made realtime multi-player games before and already experimented with storing some data on the hive blockchain a while back, the front end would be JavaScript/WASM and likely non-persistent data in sqlite or mysql. This being turn-based or at least not realtime would mean any round trip slowness wouldn't impact play - think chess rather than a FPS.
My challenge is with a mass multiplayer strategy game is one player holding everyone else up. Back in the Play By Mail days the moderator (like a DM) would take over if someone was too late responding (or the mail didn't arrive), but not sure how that would appeal to folks who might only log in every couple of days like here on Hive.
That said, @themarkymark pointed out to me the audience is so small anyway, it might be less of a problem than actually getting players in the first place.
I'm not sure I understand your game design. Could you provide a more detailed a example?
As a simple example, consider a game of poker where there are 5 players. If the 5th player doesn't log in for a couple of days, the other players can't continue so should the computer take over?
Right. Yes, you'd have to program an AI to take over for the user.