Given that these people are giving their testimony to Atajurt (and not the Chinese government), these are people trying to share their story so the rest of the world knows how bad things are. As the article says, this knowledge is either shared directly (the videos themselves are shared), or indirectly ("the information in the videos is then used by other organizations..., which documents [sic] where detentions are occurring, which communities are most affected, and who has disappeared."). YouTube is therefore preventing one of the most oppressed groups in the world from explaining how they are oppressed.
That sounds pretty bad to me.
The Google policy on PII linked from YouTube's response quoted in the article is intentionally a bit broad and vague and considers "full name" PII, but lots of people say their full name on YouTube videos. Showing ID cards isn't mentioned in the policy - those could violate the rules about addresses, but the ID documentation being shown certainly isn't accurate anymore: the people in the videos escaped the camps and I presume aren't in China anymore.
Maybe it's the documenting of the relatives still in the camps YouTube objects to. If this is a violation, would a news clip about a missing child that includes the child's name and photo also be a violation? Seems like it should be. If YouTube takes that down, are they trying to help the missing child?
The difference is that a missing child is unlikely to be punished for appearing on YouTube. The same can't be said for a detained political prisoner.
Because the disappearance would be more visible to foreigners, and therefore more embarrassing to China. It's bad PR.
IIRC, some Soviet dissidents were merely harassed for an extended period time and/or offered the option of exile, because they were so well known in the West.
At least with Xinjiang, they deny all the negative stories and have invested quite a bit of effort to push unbelievable "positive" propaganda about it. Disappearing someone who's known outside of China undermines that propaganda effort. That doesn't mean they won't do it, but clearly identifying yourself like these people did makes such actions more costly, which can tip the scales (e.g. it might save you from a bullet and land you in prison instead).
If you stay anonymous, no one may know unless the pile of bodies gets too big to deny.