100% online games in the past were perfectly playable even after developers / publishers ended support. Online only games dying is a relatively recent invention. This petition is asking for consumer protection to return to the norm where a purchaser of an online game always has the choice of being able to play it in some fashion.
A game developer could do this by releasing a server application. They could even do this at the barest minimum by releasing documentation describing how the server ought to work, to allow for reverse engineering.
The Stop Killing Games campaign as a whole isn’t asking for perpetual server access, just to ensure that games stay in some sort of playable state.
According to the 3 criteria mentioned in the article, YouTube wouldn’t need to be banned, logging in to YouTube would be banned. YouTube is still functional (mostly) when logged out, and wouldn’t violate those 3 criteria. The other services mentioned, like gaming, would be banned.