Even assuming that the concept of "game" would exist elsewhere seems like a ridiculous assumption. All of the things you are saying, even "purely mathematical" are just reflections of the way humans sense the world. Any alien species you are imagining here is just a reflection of mankind.
Anyway, since probably won't know anytime soon, and perhaps never, this kind of speculation is a bit useless. But if we ever found an alien species, it seems unlikely we would be able communicate with them any more than we can communicate with a piece of rock.
Anyway, since probably won't know anytime soon, and perhaps never, this kind of speculation is a bit useless. But if we ever found an alien species, it seems unlikely we would be able communicate with them any more than we can communicate with a piece of rock.