"In a literal metaphysical sense, they have no souls. When a person turns into a vampire, they are normally observed to lose things like impulse control and ethical restraint and the capacity to feel guilt or regret. Often they also gain destructive impulses to match. But they retain the memories, and to varying extents the personality and intellect, of the human whose reanimated body they inhabit. Some consider themselves to have continuity with their mortal selves; others don't. It seems pretty clear the one you met was of the former kind."