Last year I got dinged in the judgment for not exactly having story closure.  I'm not an expert here but having played some of the games last year they ran the gamut from complete (but simple story) to barely a game at all.  So, the answer is I don't think there's a minimum but it would behoove you to keep it simple and complete rather than ambitious and not quite all there.  As far as length is concerned mine was about fifteen minutes probably but there I really don't think this matters as much as having a complete narrative.  Like, a setup and payoff even if it's only an eight minute game.