I know I have said it before but I am going to say it again.
Aikido always looks like shitty judo to me in any of these types of videos.
So, I think Judo has more to do with Aikido (at least the principles behind it) than the other way around. I'd even go so far as to say Judo seems to be a more evolved version of what most Aikido claims to be (or could be, with more non compliant rolling).
I think the only time technique looks "pure" is when two people from the same style are engaging each other. Otherwise, the interaction tends to look more or less generic and maybe a little sloppy.
We have seen great judo throws done in the cage. We have seen nice clean Judo throws in ADCC and other not Judo tournaments.
Good technique works because well its good. It shouldn't matter who the opponent is with in reason.
Same thing can be said for other combat sports such as Boxing, Kick Boxing, BJJ, Wrestling, and the what not.
This is why that aliveness aspect is important.
But remember that in MMA, even if they specialize in different arts, the skill sets fighters train are actually pretty similar; so its almost as tho they are all using the same "style." On the other hand, if we matched, say, a chunner with a ninjer of equal caliber (don't ask me how we figure that out), we're not likely to see typical sticking hands moves from the chunner. We're more likely to see generic standup fighting, particularly if we put gloves on them.
However, I'd say they share some common elements and both arts are a good complement to each other.
BTW, Ellis Amdur adresses the OP clip in It Aint Necessarily So: Rendez-vous with Adventure. Worth reading.
They have a lot of similar elements and techniques. I think the main difference is that the emphasis is on different fighting ranges. That, and the lack of aliveness in Aikido.