Looks just like what we used to do, right down to the "one-step sparring hoshinsool" (self-defense) kata early in the video clip.
AFAICS, Choi is using basic pain-compliance and leverage-based jujutsu-waza, although some of it is reminiscent of some of the Chinese qin-na I learned from a student of Yang Jwing-Ming around the same time I was studying hapkido. There is some simple off-balancing that Choi does, which seems to rely largely on uke's unstable center.
I met Michael Wollmershauser (who narrates the video you linked) at a HKD seminar he gave in, I think, 1997 out in central Massachusetts (Athol), where he is based. It was the same mainstream stuff I mentioned earlier, and which is demo'd in the Choi clip. He had a number of his "inside" students and those from his affiliated dojangs, and a few of us "outsiders" who were training in unaffiliated HKD and/or TKD dojangs. I noted that he watched us "outsiders" carefully to see whether we had anything worth his attention; at the same time, I watched him to see whether he was showing his "inside" students anything different -- or the same things, differently -- than he was showing the rest of us.
It was an interesting day.