..."willing to lose" part.

I think with hyper competitive people there's a stubborn, defiant refusal to accept losing. You'll tend to notice that they usually win at just about everything they do, board games, cards, video games, bowling, tiddlywinks or whatever.

Everything they do is a competition and they want to win it.

Like all things there's a range or spectrum for competitiveness. Some people are as competitive as golden retrievers or baby lambs while others are Rotties or Pitbulls (or worse).

To the hyper competitive person, losing is never an option. Even backing down from a challenge is a form of defeat and therefore unacceptable.