I use definition of "censorship" that people use when they think that "censorship is bad". Because this definition implies that this kind of censorship affects everyone and they can't do anything about it.
The other definition of censorship, that also includes private companies and people restricting some materials in their own domain can also be used — that seems to be what you have in mind. But this censorship, when you think about it, is almost always quite OK. Which contradicts the inherent negative connotations that people perceive when they hear the word "censorship".
So, for the sake of using words with definitions that don't contradict their cultural perceptions, I would stick the first definition.