In a formal setting, I think this is called a "roast", when a famous person is the target of the bullying.

For sure! Nothing _prevents_ a bully from being funny, it's just that often this is not the point. And most people do not strictly try to stay in any of the lanes I've defined -- they combine and interweave the different styles. I think the purest example of "bullying humor" might come from kids in the 90s. You're minding your own business, really not doing anything out of the ordinary, and some other kid yells in from of a group "Look how gay he is!" The group laughs, but there's no "joke," and the insult has been wholly invented out of thin air; there's no epiphany for the mind to connect because the insult isn't actually based on anything. That same scenario could easily play out with an actual clever joke attached. It just often is not the case, and the laughter does not depend on the the joke existing, but is related to the attack on status.