The donkey likely can run faster at first, but it will need to stop to rest way sooner than the human.
It's the same reason a human will always win against an equine in a long distance race: If the equine does not stop to rest, it will die for lack of oxygen.
Humans have evolved in such a way that we can fully breathe while running. Thus, we can hunt large game till they need to stop in order to fully breathe again, and then BAM!