The police didn't upload they videos. It's not entrapment, and it doesn't sound like the actual content of the videos is illegal.
Instead, they had an open communication channel with their target and were able to send them various links to youtube videos.
Their theory being if they can find any user who clicked on all (or most of) those links, it's probably their target. And it's unlikely some random user would have accidentally viewed all those videos.
The actual request for the raw list of all viewers seems unconstitutional to me. Too broad, gives the police a lot of infomation about all users who watched just one of the videos. But I suspect a much narrower request where google identified the target user and past just that user's info on would be constitutional.
Isn't that worse? Essentially making Google do the job of the police and the police having to trust the work of Google for it.
The police will still get the exact same raw data of that one target user. The change just means that they won't get any data on other users.