>You are archiving it for your own personal use
That is not the usual definition of archiving. That is just piracy.
Does YT own the content? Its not exactly the same as movies, music or TV shows. He is downloading a video made by another user and uploaded to a publicly accessible website. Account is not even required to watch YT unless its +18 content. So what is Google going to argue here that user X stole users Y content and they are just good middle man samaritan?
No, they don't.
>He is downloading a video made by another user
Without a license from that user to make a copy of their video.