They were probably making a little joke for the Ulfric haters. You know, all those milk drinkers whose manhoods are threatened.

Hehe yes indeed. I originally did a search through Google to see if anyone else had mentioned this and there was a thread on another forum where someone was laughing about Ulfric having a cowardly weapon and saying that it was appropriate for him to have it.
Wells lets see he kills the high king using a shout instead of fighting him like a man, He sits on his throne never fighting in any battles and yet he has the nerve to claim that he fights for skyrim yet the dragonborn does ALL the work so yes he deserves that war axe.
Actually he did not kill the high king with a shout, he used it along with fighting with his axe (Just like how I have also used shouting in battles) He stays in Windhelm throughout the uprising, just like General Tullius stays in Solitude throughout the Imperial campaign.
They both however come out to play for the final battle.