Let's be honest, we do a lot of things that don't make sense.

And as it stands, it can be handwaved with magic as it doesn't make much sense summoning a pack of fire breathing kittens. The concept can be explained thusly

Big bad magic, omnipotent man of the magical arts developed a game. A challenge. A fight. The powerless start, and the powerful... or crafty... mainly lucky... win. To enter, he does some magic mumbo jumbo, and from then on can manipulate the person for the duration of the bout.

Essentially it's just a game, either way, not really different from any other concept. In your example, your leg would simply change, and you'd have to go with that. You could add some story to it, or just have it happen. Then deal with the consequences or advantages therein.