It’s not like proof of work at all. It’s just a challenge and response; youtube includes a random number in the webpage for each video, and expects to see a request parameter with a particular value calculated from that random number when you request the video. If you don’t do the arithmetic it throttles you to 50kb/s.

Since the calculation of the response is done in JS, and they occasionally change the formula, some download programs are moving towards running the JS rather than trying to keep up with the changes.

It’s really just bullshit to make people’s lives harder.