I have to admit, I'm still rather confused by the analogy.
Is "the game" meaning "being in a romantic relationship" or "playing with a lot of people" or simply "something more than just catch" ?
I think it's definitely possible for two people to have a wonderful sexual relationship while understanding that they couldn't work as a couple. I also believe that people can be very emotionally and sexually connected, very happy with both, and yet not have all their sexual needs met by that one connection. And sometimes people have a great sexual relationship that develops into an emotional bond without the commitment of being "in a relationship" so they have "more than just catch" but not wanting to "play the game"
I'm not sure if any of this is what you mean by "not compatible sexuality" ?
It it almost seems like my interpretation is "sexually compatible" vs "emotionally compatibility" ... having sex is part of one's sexuality. If your sex is compatible, it seems to follow that your sexuality is also?
I don't need labels to define me. They're sticky and I hate the glue they leave behind.