Death is just a daemon who brings death with him, much like how the other horsemen bring war, plague and hunger with them, and so he shouldn’t be any more immune to dying than the other three. He is not the ‘angel of death’ (or he’d be divine), neither is he ‘death itself’ or any such cliché.
Besides, Warded does not mean immune to dying, anything can die in the game through spell and skull damage. Warded simply means protection from the mystical type of sudden death that is deathmark. The fact that Death is not immune to it is no more strange than him not being immune to Poison, Devour and various other things. I mean, does “Hey, I just ate death, it was tasty! ~burp~” make more sense to you?