Well, that's an easy question. The answer is No. This isn't government censorship since the government isn't doing it. Same as if a politician asks you not to park on their lawn it's not "Government issues diktat against man for parking car".
Mafia coming to you for protection money since "bad things happen" is not extortion. They just ask nicely. The fact that your building burned down after you didn't pay is totally unrelated.
Ah, that explains why the government is going after Facebook then. They must have refused to pay the protection money. That's the best explanation.
Google has accepted over $600 million in government subsidies from Federal and State governments. Thus Google is effectively a public-private partnership and can be regulated no differently than public schools or any other public entity.