That's a good question. I don't know where fanfiction fits in the world of copyright. Does it matter that the fan work is available for free, says that it "is created with no commercial intent or gain", and openly acknowledges that Meyer owns everything she owns?
Even the similar beginning is only similar in that most events happen in Meyer's way for the first couple of days in-story. (Which makes the point of divergence more interesting.) I wouldn't consider it plagiarism, except maybe for some of the early dialogue. (Which is necessary for the author's point.) But since Luminosity's Bella keeps a regular journal and narrates the story from a completely different psychological make-up, wholly-original content is there from the start.
Which brings me to one of the main reasons I didn't like Twilight (beyond those already mentioned). I didn't like any of the characters, especially the central one. Bella is an unlikeable, passive place-holder.
Meanwhile, I haven't read any of Anne Rice's vampire novels. Has that boat sailed?