the difference between a government and a private institution is just the amount of power they have. There are places in the world run by unrecognized militia, who of course do censor free speech when they can. It's still censorship, although they are not "true governments".
So, if we have a monopoly (oligopoly) on the control over flow of information by big tech, this is effectively censorship. And if the laws don't apply to them formally, then maybe there should be new laws for that.