I still don't see why some people thought vampires were not undead. I kept stressing this in the lore forum, but none would listen. They're too caught up on the scientific aspect of it. "Herp, you can't cure death, so vampires aren't undead!"
Even before Skyrim, these sources confirmed it:
"I can't remember the dreams I had that night -- only that I was doing something horrible and I couldn't stop myself. I woke up screaming. The next night, at an inn a little closer to my destination, my sleep was deep and dreamless. On the third night, I died. Of course, I didn't know that I died. I had gone to sleep in a nice warm feathered bed and I woke on a cold wet stone mortuary slab."
Or this tale about the first pureblooded vampire. The progenitor of the vampiric race.
Violated and comatose, Lamae was found by nomads, and cared for. A fortnight hence, the nomad wyrd-woman enshrouded Lamae in pall for she had passed into death. In their way, the nomads built a bonfire to immolate the husk. That night, Lamae rose from her funeral pyre, and set upon the coven, still aflame. She ripped the throats of the women, ate the eyes of the children, and [censored] their men as cruelly as Bal had ravished her."-
Or
There was but one tribe in Cyrodiil, a powerful clan who had ousted all other competitors, much like the http://www.uesp.net/wiki/Lore:Imperial themselves had done. Their true name was unknown, lost in history, but they were experts at concealment. If they kept themselves well-fed, they were indistinguishable from living persons. They were cultured, more civilized than the vampires of the provinces, preferring to feed on victims while they were asleep, unaware.
Or
And shall we tolerate the hidden hosts of the undead, the arrogant princes of necromancers, the ancient vampire demons who creep from their lairs in the West, seeking refuge in profane Daedric shrines, abandoned Dunmer strongholds, and corrupted subterranean labyrinths of the detested http://www.uesp.net/wiki/Lore:Dwemer race? For ages the http://www.uesp.net/wiki/Lore:Great_Houses and the Temple have kept our land clean of the vampire's taint, but now these undead lords and their vile cattle have returned. These vampires must die, and their corrupt cattle with them, and their blood taint must be forever erased by fire and stake.