I was on live TV recently and wanted to keep a recording for myself, that wasn't just filming the screen with my phone. I first tried screen recording watching the show in my browser in their streaming service. Got a black video. Then I tried their phone app, got a black video. Finally, using my phone but the web page they enabled playback without DRM and I could record and store it. When more devices support DRM they will probably get rid of that fallback as well.
I bet that it Google really wanted to it could force Firefox in line, but I imagine that actually preventing screen recording would require compliance at the OS level too, and I don't think that even Google could demand changes like that to Linux. Best they could do is block Linux clients from YouTube, but user agent spoofing or emulation could probably circumvent that.
And even if Google does somehow manage to entirely block screen recording, we can always exploit the analog loophole.
The GPU would simply return all zeros for area where DRM-protected video is being played. Duh.