Apparently, the purpose of an Infinite Game is not to win but to continue playing the game.
Some say Evolution is an infinite game. It probably means that in Evolution, winning means getting a chance to continue to play. If you win (survive), you will continue to play, but, if all others loose, you will inevitably loose. So, I think good players not only should strive to survive, but also try not to let other players loose so that the game continues in full vigor.
If you haven't realized the purpose of your life yet, you might as well treat it as an Infinite Game in the sense that the purpose of living is to continue to live... I mean to LIVE!