[Hallucinaut]

There is definitely the concept of the anti-joke. Anti-humour has the wiki page.

The sadly-late Norm Macdonald was a good proponent.

Fwiw though I watched this after your post and I'd say that's not really the same. I'm not sure what you call this technique in speeches with such a setup but it adds great emotional gravity and is something I see and appreciate a lot in speeches like this (or even shows like The Good Place which is incredible but can't be described further without spoilers).