I'll vote story, but I disagree that it has to be epic. That's just one way of doing it. I've always approached roleplaying games with an "author's eye" if you will. I think of my characters, plots and settings the same way I would if I were writing (or reading) (or watching) a novel, TV show or movie.
That said, I like to watch action movies. Before I saw your definitions, I would have picked action, but I don't like the kind of action you're describing; that seems kinda random, disjointed, and unconnected from any plot, or even from the setting, if you're really serious with the "like Diablo."
Anyway, I guess I'm saying given your descriptions, I'd say story first, and the other three all tied for a relatively close second, but that at the same time I quibble with your defintions; I wouldn't use them.