if you really want to make a DMCA complaint against youtube they will honour it, but they try to push all requests through their own DMCA-alike system that lets copyright holders file takedown notices, but it doesn't have any legal standing under the DMCA or any other country's copyright laws. the youtube takedown notice system is basically "if you ask nicely we'll take it down".
Sure, the YouTube (not Chrome Web Store which is a completely different organization) system requires far more of creators and far less of "owners" than DMCA specifies with respect to copyright. We're still talking about copyright. The extension under discussion cannot be construed as violating copyright, or even facilitating violation of copyright. That's why even the crazy overblown threat letter doesn't mention copyright. It probably would have, even if it did so without justification, if the end goal had been to take down a YouTube video. The end goal in this case was actually to take down a Chrome extension, which is only similar in the sense that the people who make such a decision also work for Alphabet.
if you really want to make a DMCA complaint against youtube they will honour it, but they try to push all requests through their own DMCA-alike system that lets copyright holders file takedown notices, but it doesn't have any legal standing under the DMCA or any other country's copyright laws. the youtube takedown notice system is basically "if you ask nicely we'll take it down".