Technically, since YouTube is a video site upon which you stream (download) videos, capturing that stream and storing it isn't really doing anything want.
YouTube isn't exactly happy that you can do that, largely because they want to sell you that nice feature on YouTube Red, and downloading MP3s (or M4As for the civilized among us) full of YouTube music is something that almost everybody has done.
I mean, you are downloading the content to begin with. It's being stored locally, but then deleted shortly after. You're just not getting rid of the information after you receive it, similar to how TV recording works. Recording something you can be sent instantaneously (or near instantaneously) is not illegal with my (unprofessional) knowledge, and in my nation, as far as I know.
What I normally do for downloading YouTube videos is just go to a random YouTube downloader site off Google, and try it. If it doesn't work, onto the next one.