I do like the lore of this character. Recoiled at it at first, because yeah, Warcraft, but it's growing on me. I think I remember saying to someone that I'd like to see a demonologist character, but I was thinking of a more magical class than someone who actually uses demon blood to burn things or something. But this is better than magic, because demon teeth explode. There's no willingness to bargain with or appease demons at all, just mash them all into hellspawn-brand explosive goo. Plus there's a secret society vibe to it, the way you can't be recruited unless you survive intense demon attacks. I like those parts. It's my favorite of the 5, from what I've seen this far.
The armor covers her, but it looks very intricate and probably magical, which I think is a mistake. This character would do better with simple and effective protective gear, like the paladin in D2. The recoil on those hand crossbows looks far too intense in the cinematic, but hopefully this won't be a problem in the game. I wouldn't mind having to use crossbows for some of those abilities, but I expect to see other weapons too, like with the Amazon. And finally, it would be pitiful if it turns into an emo goth (read: sparkly vampire) class. I could see people talking about Twilight whenever a Demon Hunter is around. *shudder*
Things I'm sitting on the fence about: glowing eyes, popularity, writing. Eh, we'll see.