Liberalism in the broad sense and its attitude to speech suffer from a sort of dualism that's hinted at in the second part of the article. To maintain traditionally liberal views on speech you have to somehow convince yourself that speech and actions are different things.
But in reality there is no such distinction and I think in our information age that's become quite obvious. There's nothing privileged about speech, it need not even be human in origin any more. Speech acts are just a means to effect change in the world, it's information in a network directed towards certain ends akin to Klausewitz pointing out that war is just politics by other means. Violence and speech but more generally action and speech are materially the same thing, one is kinetic and the other isn't, but the goal is identical.
I think the same is true in regards to money. Speech has entirely been commoditized and it's produced the same conflict under liberal frameworks that violence has. If speech is reach then it is just power and doesn't live in some lofty magical mental space.
So the title is right, in liberal societies speech cannot be violence but this is just an instrumental claim to make liberalism work. In the same sense how John Locke had to adopt a Tabula Rasa/Blank Slate view of individuals to justify Natural Rights, which scientifically turns out to be just wrong.