No meaningful definition of censorship limits it to anti-democratic government-instituted censorship.
Censorship is the ereasal or limitation of communication. If I'm quoting your post, and replacing a word with asterisks, then by most common definitions, I am "censoring" your line. If I'm asterisking out my own words, I am prcticing "self-censorship". When the Escapist is deleting forum posts, they are censoring commenters.
I'm not saying that all these forms of censorship are wrong, they might be necessary, but first of all we need to admit what it is. If you are blocking comments from your youtube page, then you are censoring your youtube page. You are limiting other people's communication. And just because you do it in a way that is within your legal rights, doesn't change that basic fact.
To deny that, just because censorship sounds like such an unpleasant word, is a pointless euphemism.