Brian Leiter
argues it's because the philosopher, unlike so many of his contemporaries, was actually a great writer:
He’s a great stylist, he’s funny, he’s interesting, he’s a bit wicked, he’s rude. And he touches on almost every aspect of human life and he has something to say about it that’s usually somewhat provocative and intriguing. I think that’s the crucial reason why Nietzsche is so popular. Indeed, he’s probably more popular outside academic philosophy because he’s so hostile to the main traditions in Western philosophy.