Regardless of the misapprehensions of the article writer, the right to free speech is not merely some lines on an American republic's constitutional document, but a philosophical concept that predates the formation of the united states by several centuries.
Facebook is a private entity, yes, but by how far it has inserted itself into the every day lives and communications of individuals around the world, it has become a quasi-state; a government in all but name of a vast and diverse demos, to which it provides services across borders, and over which it exercises incredible power in ways that traditional states could only dream of. Facebook can, at the flick of an SQL command, completely destroy the lives and livelihoods of thousands by removing their business pages, through which they - at facebook's own encouragement - conducted the majority of the economic activity, or by cutting them off from friends and family, who may have no other means of communication than through facebook's service, again because of the way facebook has encouraged and manipulated it's way into being the sole form of communication for many.
At this point, facebook is no longer merely "a private corporation". It has, by dint of its invasion of the private and public lives of so many people, a responsibility to enforce and uphold the rights of the people it claims to serve. Instead it acts as the arbiter of "acceptable" speech and behaviour, to a standard far more restrictive than any free society would otherwise tolerate, censoring almost at random, according to the whims of an unknown, unaccountable minority within the corporation.
The same standard can be applied to google, amazon, and a few other world-spanning communications and tech corporations. They have moved beyond mere "private" entities. The argument of "private property" can no longer apply, any more than it could apply to a company town enforcing private scrip and the company store on its denizens.