As for other browsers: I guess that you'd still be able to access my website, but YouTube and GMail will just show you a generic "This browser is not supported" or, at best, "Your browser had been deemed insecure. Please use a secure browser".
If we go full Nostradamus the most likely result is that Safari will play ball (because they are already doing something similar), Firefox will play ball (because they no longer have a spine), they'll implement whatever Google says, and yet another portion of the web will be closed to those who don't dance to Google's tune. I hope you're not too attached to youtube-dl or your adblocker.