Well, when Kamui was talking to Fai under the water he said "Then does it belong to that hunter? Since Subaru gave his blood to that guy...", so it's easy to assume he's a vampire as well. If it was
just Subaru's blood that was given to him, unlike Fai where it was mixed, it would explain why Kurogane said he had the eye of a murderer. Why else would Kamui think that Syaoran was Seishirou's "E", when they're supposed to be used as food for vampires.
We know that Seishirou was asking about immortality, but we don't know if that's really what he's seeking. Yuuko said that Subaru and Kamui aren't immortal, so maybe Seishirou has his facts wrong? There's still quite a bit we don't know.