How would a one-way hash even work? They already have a database of views for a video by its ID. If they hash those beforehand that solves nothing. They have the actual ID for that hash - they have to, cause they need to provide you data on it.
It could work similar to how haveibeenpwned works - send a prefix of the video ID and respond with a list of all matching IDs with that prefix. The server only knows the list not the actual video. The client can pull the correct ID out of the list.
A lot of trust they don't keep a map from hash->id behind the scenes though for data they already have.
Hell, a YT ID is 11 characters in a base64 character set. While a lot of possibilities, I do think the entire domain can be precomputed for some amount of costs.
That's not a very honest way of phrasing whats happening there. Sure it "leaks" that you are retrieving this VideoID from this IP, but you make it sound like it's sending your youtube viewing history to some random website.
Either way, I'm fine with this type of "leak" of data, as it's fundamental to an open web and can't be easily solved without cryptographic/hashing hoops. What's next, you want anonymity from the server that you're requesting content from, really?