This looks good, I'll give them that. The fact that it flows so well, not a good thing. It doesn't seem that challenging. In my opinion, what would look better would be if they added a darker demonic tone to it.
The World should be screaming and screeching at Dante, not writing silly notes on a wall for him. The walls should ooze out blood, even spit it. And should spit poison, and actually crush and impale you. Watching the trailer, DmC Dante just gets away without a single scratch on him. The rubbish cans moves around, they didn't hurl themselves at you. Dante should be getting hit and hurt, and you should either have to wait until he heals himself (By not getting hurt more) or you should slide down and catch some health. And if they're taking inspiration from previous Devil May Cry games, why not have it so if Dante does fall off the edge he lands through a portal which has him face some difficult enemy or whatnot. And when he defeats it, he returns to the previous point he was at (They did this in lots of Devil May Cry games).
I like the ideas they're going with, but they could make this more darker and more brutal. Not thoroughly impressed.