I don't think its about entitlement, but competition and increasing value of loss.
The more you win, the more reputation you feel you have as a winner, the more you stand to lose if you don't win. The only thing that makes you a winner is one thing...that you win. Losing the game is a much greater loss than winning is a win.
I have seen some other studies where it was found you could greatly influence people's answer to a question simply by phrasing the same data either in terms of loss or gain. The constant trend was that people chose to avoid loss.
also, there is another phenomena where people who are expert in a thing know what they don;t know. Sure, I won that magic game, but, I was sitting in my seat...I know I got lucky and top decked that card. You just know I won. So, I now have an image to uphold, and a reason to doubt that image is true.
So really, I don't think its a matter of entitlement but the opposite.... if you don't feel entitled to the reputation you have, and want to live up to it. You have people seeing you as a winner, and you already don't deserve it.... why lose it?
This is also why, I think, you don't see the same in self-challenging games because, you can't actually consciously cheat yourself, you know what you did.
I also think, as a loser, there is less incentive to see the competition angle, and more reason to see it as a matter of self-competition. "I can't beat this guy, so I will try to score better against him than I have before...and that is a private win for me" makes a lot more sense when you are not winning the matches.