The term "vampire" is widely used in many different ways. In some versions, they are demons, in others they are just superhuman beings infected with some sort of virus that makes them drink human blood... and everything in between. I read Dracula a long time ago and the book does sort of hint that Dracula had some sort of relation with devils and such... so....
Anyway, that game reminds me of Kingdom Hearts, the ground combos look a lot alike. DmC may have a lot of similarities to this game, but they obviously took most of their ideas from, believe it or not, previous DMC games... The whole alive city and different dimensions and stuff was done for the purpose of explaining previous unexplained details in DMC (like the red string things) and to make the world more believable. I mean, in DMC3, a huge tower came out of the ground a killed everybody but the world gave zero ****s about the fact and nobody, except Dante and Lady, went ahead and tried to do something about it.