I succeeded in slowing this down in a way that appeared useful for the purpose intended.
1. I downloaded the best-quality version available of the video (in this case mp4), because slowing down always makes the quality worse so might as well not compound the problems. (For downloading, you use whatever works. I used a command-line utility for Linux called youtube-dl. It doesn't matter much; successfully getting the file is what counts.)
2. I played it in VLC and pressed the "play slower" button till it got down to quarter speed. (It will go even slower, but I didn't try that.)
(VLC is free, and will run on all commonly-used systems - available from the VLC website
The sound was not nice, quite choppy, but it was OK for transcribing in my opinion. My computer is a few years old and had a cheap & slow processor even for that time, so anybody with a good computer could expect results as good or better than what I got.