It's not a stretch at all. They want to punish words as if they were violence, i.e. put people in prison, send armed men to arrest them forcibly, etc. That's at the very least. This is openly stated, "some words should be illegal" is 1000% a sanction on violence against people for the words they speak.
In your examples, you get it right at the end: we seek to contextualize actions and use peoples words as evidence of context. It is the context of the acts that matter, not the words said.
In your examples, you get it right at the end: we seek to contextualize actions and use peoples words as evidence of context. It is the context of the acts that matter, not the words said.