If the "game" is survival and selection for attention (to get compute space, so literal survival) from humans, "interestingness" is what will matter and I think what people will end up finding most interesting is NPCs that feel like other identities they can empathize with and interact with -- work with to build things, spend time in a community with, fall in love with and so on. This really is about virtual world construction more than simple competitive games. I think it may not end up looking like any particular sense of "AGI" we can currently imagine (I really think we can only properly imagine it exactly when it exists, and it seems not to yet), but it will probably be "distributed" enough that the interfacing may not feel like anything at any one particular site.

The game may even be played by saying things on Twitter and becoming interesting enough that people DM you and try to build a relationship with you, while you're a bot.