Yes it does. Dying is a creature going from the battlefield to the graveyard. Doesn't matter if you killed it with a Doom Blade, if it died in combat or even if there was a legendary creature in the battlefield and one of the players plays the same creature. However if the creature is exiled with something like Path to Exile, now that isn't dying and it doesn't work for morbid. Usually it won't matter but once in a while it will.
In Innistrad limited Sever the Bloodline and Fiend Hunter don't work for morbid. Moldgraf Monstrosity does work because first it dies going to the graveyard and only after that you exile it.