I think it is highly questionable of Twilight even counts as literature in the first place, but that's behind the point. Even if we drop the wort "literature" and just debate if Twilight is even Gothic or not, it still is complete fail.
Twilight is 100% romance and nothing else. Tossing a sparkly dude into a book and arbitrarily deciding that's a vampire doesn't automatically make something Gothic. Even if you can prove legitimate supernatural overtones, that still doesn't give Twilight membership to the supernatural club. You the atmosphere to be dark [and scenes taking place at night time don't automatically count] and even a bit macabre.
Real examples of Gothic would be anything written by Edgar Allen Poe or all of Edward Gorey's art. If you're not familiar with the latter, he did the intro art for the old Mystery tv show [see below link] among many other things.
http://www.youtube.com/watch?v=rAmGsM4Dids
If Twilight was Gothic, the book would be about Edward having to deal with the sheer unnaturalness of being a vampire... while Bella is on the brink of insanity due to her own self discovery that she is both attracted and repulsed by both him... and maybe even her own behavior.
