I don't think all life is a game in this way; with a game we hold ourselves to the rules
for their own sake - the pleasure we get from play is that of acting within the sandbox we've defined. It is a sketch of life, a model, a way to explore an idea. In the context of a game we might be adversaries, but I am intimately aware of the boundary, and that we are at play - our adversarial relationship is not "real". We often say, "It's just a game", and the
just is crucial to the difference.
This is different from social mores, which are boundaries we respect because transgression has consequences we care about. There are real ends; it's NOT just a game. There is no space or context beyond what happens in life, as there is in a game (taking place within the shell of the true life).
The purpose of play, and playing games, is to prepare us for the actual contests with outcomes that we are invested in.
Of course we might USE play, and games, as tools in the course of achieving real ends (like the Olympics as a goal for furthering peace), but this is different from those ends (peace) being a game in themselves.