If the player is allowed to bet for themselves surely will not throw their game, they will even try to perform their best because it has a double reward, the ranking, and the winning while on the contrary, if the player is allowed to bet on the opposing team or opponent, then this will only mean that the player might throw his game.
I believe that professional athletes are originally not allowed to bet either for themselves or their opponent because often times this kind of thing if allowed gives negative impact to the game performance of a player but somehow there are cases where players are allowed to bet on other games not affiliated with them.
Yes, they can bet on other sports.
I like the idea though of letting them bet for themselves, it gives more adrenaline to the player/fighter to win the game at any cost thinking there is also their money on the line.
But either that is not allowed by most of the sports industry organizations. Perhaps there should be revisions that could happen in the future as the gambling industry is getting bigger with easy to access online gambling sites.