The fact that there might be other places a song can be sung isn't the point. If you tell a singer, even in a private party that they can't sing this song but can only sing that song (I mean insist, not just request), that's an act of censorship.

It might be a perfectly reasonable act of censorship, and you might have every right or even duty to do it, but that is a completely separate matter.

"Censorship" isn't just confined to the situation where the person doing it has absolute power over all methods of communication. It just means they have power over some occasion, and use it. And they might do it for all kinds of reasons, including commercial considerations, or ethical consideratins, not just politics.