Yikes! I'd say that looks like dirty heads to me. Dirty heads tend to have streaking that tends to originate off of high-contrast areas and go to the left. Look at the fluorescent lights in the video as an example of how the streaks like to start there. when you see that extreme horizontal shaking, that's probably the tape partially sticking to the heads.
Your camera is interesting in that it'll even display that picture at all, many prefer to just go to blue screen when the video is that unstable.
Also, what type of tape (brand and tape type) is that? I've heard Sony HMPX tapes in particular were extremely bad. There were certain Hi8 tapes that degraded terribly and liked to clog heads, so I wonder if that is one of those.
See this video for an example of a tape that clogs the machine every few minutes:
https://www.youtube.com/watch?v=6qJJyxwxly8
If cleaning the heads doesn't work, it's also possible that the heads are worn out