Like I said, it's not about the outcome. That also means "opponent" has zero negative connotations. You do not desperately have to beat them, you just try to because the attempt itself is fun. And what's the point of a relationship if not having fun (more fun than you would have alone)?
That everyone isn't wired that way is obvious, a lot of people either care too much about winning, making them bad losers (and worse winners), or not enough about playing, so they aren't giving their best, which makes it unsatisfying to try and beat them. I dunno what I would list as requirements to be that kind of person. A healthy dose of self-assurance might help to be able to shrug off losses, but I don't think that's really it. Perhaps it's a certain (emotional) distance that makes it impersonal, quite in the literal meaning -- not about the person. If everything is personal for you, you'll hardly handle losing (and winning) well.