If you choose one sub-game, then there's optimal play for that; if you switch between them, then there's still optimal play, it's just you need to weight it if there is no canonical ultimate score (just like with utilities).

If there aren't any scores or sense of progress at all, I question whether it's a game at all, or whether it merely bears a Wittgensteinian family resemblance. If you and I push around piled pieces on a Go board just for the pleasure of watching the piles build and collapse and form swirling patterns, we're doing something entertaining (maybe) but who would call it a game? To call life itself a game is to either commit a tired weak metaphor, or to drain the word game of all meaning.