The basis of the argument is that “the right to free speech means the government can’t arrest you for what you say.” In the context of capitalism, that’s an incredibly reductionist definition. If speech is supposed to be free, we must ask: who owns the means by which speech is expressed and transmitted in the modern world? Who owns the newspapers? Who owns the TV channels? Who owns Twitter? Who owns Facebook? Who owns the film production studios? Who owns the ISPs? And so on. The answer is always the same: not the government. Not the people, either. All of these things are owned by capital. All of these things are industries.
So, in a situation where public discourse takes place in privately-owned spaces, how are the handful of people who ultimately own most of the media any different from a government? Apart from the lack of any kind of system of democratic control or a pretense of accountability, that is.
...Ultimately, what this comic is selling is a strange libertarian capitalist fantasy of freedom, where freedom is defined solely as freedom from government interference, but freedom from the structures of authority produced by the accumulation of capital is never considered.
The value of the argument aside, it's a fun bonus to imagine how many of XKCD's readers would likely be mortally offended at the suggestion that they've internalized libertarian capitalist values.