I have a really broad definition of horror, too, but like metternich I believe films can legitimately be multi-genre. I consider genre classifications to be additive, rather than exclusive. I consider all of the films on your list horror in some sense.
However, for the sake of discussion, if I were to give each of those films one major genre, it would be this:
Battle Royale - Adventure. Although since body parts get splattered all over the place, and children are killing each other, I'd say it's also a "gore" film, which isn't necessarily horror, but usually is. And also an exploitation film.
American Psycho - Black Comedy. Although since he murders people violently, it's a good candidate for being classified as Horror -- the psychotic killer variety, ala Henry: Portrait of a Serial Killer (subject-wise, not tone-wise). Since the movie is about the killer, not the victims, to me, that doesn't meet one of the core qualities of a horror film. I'd put it in the same realm as Sightseers.
Donnie Darko - Drama. However, it's also *almost* equal parts Horror. The film truly is about the victim, tormented by his own psychological plight. And it's pretty dang creepy. This one was the toughest choice for me.
Predator - Action. And to a lesser degree, Sci-Fi. However, I agree with metternich that it's like a slasher, and you could make a case that it's Horror at its core.
Terminator - Action. Although it contains plenty of horror elements -- not as typical as Predator though. Also, obviously, largely Sci-Fi.
Se7en - Crime Thriller, based on its primary plot structure. The detectives aren't really under attack by the killer, and you only find out that they are via the twist. However, it's hella gritty, and extremely influential to the post-2000 horror style that uses that crisp, desaturated look with disturbing set pieces. It belongs on horror lists, of course.
Silence of the Lambs - Crime Thriller, for the same reasons as Se7en. The main character (Clarice) isn't really under attack by Hannibal, and she's the one chasing Buffalo Bill, not the other way around. It's not structured like horror. However, the violence is darn close to horror, and Hannibal is an iconic villain in the horror genre. The scenes with Buffalo Bill qualify as horror scenes, it's just that we don't really know his victim, as she's not really a character in the film, so we don't really see it from her perspective. I do think it's closer to horror than Se7en though.
Cape Fear - It's been too long since I've seen this one, so I won't really comment. I don't remember considering it primarily horror when I saw it though -- more of a thriller with a really bad bad guy.
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