Parodies are protected, fanart is not, so any copyright holder can shut down a fan's website on those grounds alone if they really felt like being an ass, which I've already seen Nintendo do with some Metroid sites.
Besides, does it matter if they have decent legal grounds or not? Unless you're a respectable corporation or part of a class-action suit, nobody has the resources to stand up to Nintendo in court, so with a scary letter that blurs a few lines (which Nintendo does in every instruction manual they print) they can bully anyone to get their way. A half-dozen websites aren't nearly a large enough scale to phase them.
Also on DeviantArt, Rumble, DLive.tv, and the Fediverse (@freespeechextremist.com and @bae.st)