I think that's the catch, and Google (or their lawyers) are trying to interpret it more broadly than it appears to be. I also took it as Youtube could use the videos for promoting the Youtube service, but other Alphabet properties don't fall under that ToS.

Then again I'm not a lawyer so I could be completely wrong. Hopefully this gets sorted and the guy gets properly compensated. It's not like Google can't afford it, and it would be positive publicity for them. Of course, it could also set a precedent and they would face lawsuits from other content creators, so I can understand their desire to fight it.