On the one hand, violence is always a threat to speaking freely. This is not new. At the very least getting fired is what most people can expect if they speak freely about legitimately confidential things at work. Even things like disparaging co-workers, in a public setting, or harassing people at work by saying inappropriate things can get you fired.
You are free to speak freely, but there are consequences, Free Speech does not imply uou can say what you like consequence free.
In some (criminal) industries, speaking freely will get you killed. If Hollywood is to be believed, speaking against the rich and powerful can get you killed. (I suspect it happens, I suspect its nowhere near as common as Hollywood makes out.)
To your point though Free Speech (capital F) has a specific constitutional meaning, and covers the consequences the govt can apply to your speaking freely. It does not promise no consequences by companies.
There is no threat to Freedom of Speech here, because what he was doing was not that kind of speech. Of course there is a chilling effect on speaking freely, his speaking out had consequences (regardless of the hand that pulled the trigger.)
In short you can't just say whatever you like (as E Jean Carrol understands) without consequence. That's not what Freedom of Speech means.