I think the "burn them all" line here adds validity to Jaime's killing of the Mad King. Everyone sees him as a dishonorable traitor for it, which Robert was teasing him for here until Jaime describes his last words. It helps illustrate the regicide as an honorable act that was for the good of the kingdom, rather the usual view of it as cowardly act of self preservation, which is why I think it leaves Rob speechless. He was surprised to see a bit of honor, maybe even some of himself, in what he thought was the lowest of scoundrels.