How do YouTube downloaders access the videos?

I did find this answer but it uses YouTube's APIv2, and is now outdated as stated in the answer.

YouTube's terms of use state that you can't use another player or download videos, so it makes sense they've excluded it from the API.

Knowing that, how do online YouTube downloaders, or third party Android apps (that allow to turn the screen off while they keep playing music for example) access those videos?

I'm trying to access a video to stream it inside unity for example (by the way there's a couple of unity assets that do it too), and I'd like to learn how they do it.