Fortunately we seem capable of narrowing our memory to "where we are now", so I have little doubt that infinite beings can keep ourselves entertained.

Even so, it would be nice to have a meta-scorecard for those in-between moments. I mean, I'd like to know if I ever cheated an entire country, became their great leader, and converted otherwise well-intentioned people into willfully-ignorant follower. As games go, that would be quite entertaining.