>1 a : the institution, system, or practice of censoring

>"They oppose government censorship."

The example use calls out government censorship as a specific type of censorship. If "censorship" meant "the government censoring things" you would not need to specify "government censorship" in that sentence.

Yes, I know that dictionary definitions are not necessarily the final word on what something means, but they're absolutely correct here. It is a broad word and it is widely used in other contexts. People other than the government can censor things.

For example: https://en.wikipedia.org/wiki/Corporate_censorship