Ok, after doing more research, it appears that either version should work. "Ganar" and "ganarse" are used interchangeably in many situations unless the "ganar" has an object, in which case the "se" could not be used. http://forum.wordreference.com/showthread.php?t=1965391
So I guess it could be used, but it doesn't have to be included.
I also found this forum about this topic interesting. Not sure how accurate it is though: https://www.duolingo.com/comment/1292636