In AmE "thanks for the game" is often used after a "pick-up" game of some sort. For example, you and a few friends are dribbling a basketball and shooting baskets on a public court but there aren't enough players to actually play a regulation game. A group of passers-by see you and ask "Want to get up a game?" and you agree. Now you've got enough players to form two teams and play a regulation game of basketball. When you're done playing, you would typically tell the newcomers "thanks for the game."