It's very interesting... if only mostly because Sakurai is creating the entire mythos from this game more or less from scratch. Besides the original game's "You're an angel, you hate medusa." that's all their was a for a story.
That said, while I'm interested to see the story he comes up with (lots of hints throughout the trailer) I'm also a bit worried... Sakurai has never really done anything where the story can play a serious role in game development. I mean, before this all he really had to his name are the Kirby series, which only has the most basic and kiddyish stories, and Smash Brothers, which mostly throws story out the window. Even Brawl's campaign mode wasn't really written so much as it was rolling a dice and seeing which characters would be fun to have minimal interactions with.