Some private properties really are part of the public sphere, counting for the protection of free speech. The main example being printed newspapers, that will print opinion pieces sent to them, even when they go against the private owner's interest, even when the opinion piece comes from a political enemy. They are privately owned public forums.
Other examples of public spheres in private hands are the internet provider you're using to read my comment and write your own reply. The ISP doesn't interfere with your free speech. E-Mail is another great example of a public sphere. You can freely send your opinion to any and all the people you want.
In some countries, all unexploited nature is considered public space. Trump's Twitter was deemed a public forum.
It has nothing to do with government ownership, even though most physical public forums are government owned, such as parks, streets and squares.