Ardia, how do you define playing a game? Is saying "please" and "thank you" a game? This is just behavior we learn to make our lives easier. Most human interaction involves customizing ones behavior to get a wanted response. I personally draw the line at dishonesty and insincerity. I find it hard and distasteful to say things I don't believe and to act in ways I don't feel. But my suggestion to not promise sexual fidelity doesn't require this. The game playing needed to seduce women does require this, which is why I cannot seduce women and why I prefer marriage.
Does this apply in a 'CoAlpha' society as well? Yes, I think so, this is about fundamental human nature.