It's not. This seems to be yet another person who is very confused about what the first amendment says (despite it being only 45 words long and written in plain english).
You're correct, but are being unduly harsh. Reading the text of the First Amendment only gets you so far. For example, it says "Congress shall make no law...abridging the freedom of speech." But guess what? It also applies to state governments, actions of the executive, public schools, and all sorts of governmental things other than laws passed by congress. And don't even get me started on the universe of legal nuance packed into the other words. (What is "the freedom of speech"? What does it mean to "abridge" it?) And these are just the ten words of the speech clause!
You're right that it (mostly![1]) doesn't apply to private parties, but the text doesn't tell you much about what the First Amendment does and does not apply to these days.
[1] There are some fringe cases where a private company takes on some First Amendment obligations by fulfilling the traditional role of government, such managing seemingly public spaces.