It was Trayvond the Redguard (what a name) and he sells Summon Scamp, but yeah, an amusing oversight nonetheless.
You're making a lot of incorrect speculation today. Undead most definitely have souls:
Vampires have always been described as undead, because that's what they are. They're certainly not alive by the standard definition. And it really doesn't matter that they can sire children, as there's nothing in Molag Bal's curse that says they can't. Liches, again, are undead beings of their own making. Both of them have souls, as evidenced by the fact that you can trap said souls.
I don't know, I still don' t remember it being mentioned zombies or skeletons have souls. I DO remember, vaguely, something regarding it, and so I don't say they don't with full confidence, but oh well. Even with the transcript you provided, I am still not inclined to agree. Especially since Dunmer summon ancestral ghosts, not zombies or skeletons to do their work. So it seems contradictory to use an example of a race that commonly summons the ghosts of ancestors, and doesn't seem to use it with bones or flesh.
But speculation is speculation. It technically can be correct or incorrect, but its speculation. Specifically, mine is based on what little we do know. So who knows?
Regarding Vampires, I know there are many within the TES universe which regard them as undead, but I wouldn't personally if I were a person within TES. How is a vampire undead when they don't seem to die? Yes, there's the mythos of "died and rise again as a vampire" that is even seen in game after 3 days, but I don't believe it is literal, but metaphorical. If you've seen some of my posts before regarding it (I think on my older account, which means the posts were from 2009 or so, I think), you'd see how I come to believe that and attempt to explain it (One of the things that garners distaste for my posts lol). Also, what other undead can reproduce? There is no other undead like a vampire in any manner. There's simply not enough evidence for me to classify them as undead, whereas there's plenty for others. This is personal preference, though I also would like to suggest that it is open to debate lore-wise.
For Lich, I find it hard for myself to argue that they are not undead, even though I stated otherwise. It is entirely a person, with their own body, and etc. The only difference is that they live longer/indefinitely. They do not appear to have any biological functions (what COULD be considered biological within the TES universe), or anything else. But I can't in good faith call them undead given they are not dead and have not been dead. How can you call something that cannot die, due to age, I.E. a vampire in our world being called undead) undead? Why can it simply not be a living immortal? Zombies are animated dead, and this is what it means to me to be undead. It means not dead but not alive. Well, to be dead means to no longer be animated (alive), and living means to be animated (not dead). Things that are not alive typically are not animated, they're static. And yes, this is the TES universe and blah blah blah. The point I am trying to make is that Vampires, and somewhat for Liches, are more living than dead, especially since they have a soul and are conscious of their environment. Or, in other words, how can a living person (who became a lich) become suddenly undead yet still be able to live in the corpse? Is he living or dead? Paradox?
What are the exact criteria for being undead? I provided my opinion. And it's not an attempt to rewrite or change TES Lore, and a lot of people mistake me for trying to completely throw it aside, what I do when writing about Lore is how I would feel if a person within it, or that I treat the lore as it is our real world and then start writing.