Chess dot com doesn't violate (let alone control) free speech. They manage it 'cuz there are under 18's who enjoy playing this game.
Remember, they're out to make $ (good for them !)....that's why they called it a "com" (commerce ?).
This site is morally responsible and good policemen. We need it my love's.
The First Amendment prohibits Congress from passing a law abridging the freedom of speech. It doesn't prohibit Chess.com from censoring material that you submit to their site.