Welcome to the DMCA. It's as broken as copyright and causing quite serious stifling of young creators. It sometimes feels like it's used more for evil than for its legitimate purpose.
Knowingly making a false DMCA claim is perjury, and IMO it should be treated as such. Instead companies send out automated claims in the thousands and then come back with "but we didn't know it was wrong, it was the bot!" and get away with it.
That's exactly what it is used for. It's a multibillion dollar industry that will always ask for more and more power to police their imaginary property. They even coerce other countries into adopting similar laws as part of trade agreements. I'm convinced that copyright infringement is moral and akin to civil disobedience.
If a group of us formed and we did this to all of them and gunged up the system, google would be forced to improve it.
This might work between rival game streamers or something but the law offices of Dewey, Cheatem & Howe likely do not have a YouTube channel for you to retaliate against.
Even better if you created a "burner" corporation. Ie P.O. box in Delaware and act on their behalf. They have to take you seriously because corporation, amirite?
IMO the way to go is to get their contact details out of the copyright claim and sue them in small claims court.