I don't have any strong views on whether this user should have been given a temporary ban vs a warning, but (unless the ban was for a comment which is now deleted or a private message, which are each possible, and feel free to correct me if so), from reading their public comments, I think it's inaccurate (or at least misleading) to describing them as "promoting violence". Specifically, they do not seem to have been advocating that anyone actually use violence, which is what I think the most natural interpretation of "promoting violence" would be. Instead, they appear to have been expressing that they'd emotionally desire that people who hypothetically would do the thing in question would face violence, that (in the hypothetical example) they'd feel the urge to use violence, and so on.

I'm not defending their behavior, but it does feel importantly less bad than what I initially assumed from the moderator comment, and I think it's important to use precise language when making these sorts of public accusations.