I'm definitely of the belief that any ending to a game still counts as beating it. For example, in the original Wario Land, I don't see any reason to require the best ending. Even if you get the bird house ending (I think that's the worst ending), you've still completed the main part of the game and the final end boss. That should count in my book.
But of course, there can and should be exceptions. I don't think it's unreasonable to not count the "joke" ending of Wario not getting out of bed. I also wouldn't count games that end half way through if you are playing on easy (like Magical Chase). While I'm 100% against games penalizing you for playing on easy, if the developers choose to cut you off at the half way point, then you should have to play on normal to be able to beat the game.
These are just my opinions and I'm not overly attached to any of them. If the general consensus disagrees, the person running the contest, can set the rules as they see fit and I certainly won't lose any sleep over it.