Bram Stoker coined the use of the term 'undead' to refer specifically to vampires, and since that's actually part of the Castlevania canon, I'd assume CV vampires are undead.
As for mortals, as said before, I'd assume that people actually have to die of something before his powers as Death come into play, hence him needing to defeat the Belmonts conventionally. Walter had already died of becoming a vampire, didn't have a soul anyway, and so was fair game.