If you received a death threat on hacker news that listed your full name, and your kids' school addresses, wouldn't that give you a panic attack? I'd call that harm without a doubt.
While a threat doesn't actually do any harm to a person, it does ruin discourse.
Reason being that some people are more sensitive than others, and will not post things that they feel are controversial or personal since they feel they'll be challenged or threatened for it. Even if those threats are completely bunk and amount to nothing but trolling, the chilling effect on discourse is still there.
That's the way to solve that issue.
And if using a threaded system like HN,/.,Reddit, etc, if the threatening post is the only response to a comment, downmodding it doesn't accomplish anything.