"Dies" just means "goes to the graveyard from the battlefield." Did another Zombie do that, for any reason? Then the Diregraf Captain's ability will trigger. Doesn't matter why the creature is going to the graveyard.
Here are the full definitions, if you're interested in the specific wording:
700.6. The term dies means "is put into a graveyard from the battlefield." It is used only when referring to creatures.
701.14a To sacrifice a permanent, its controller moves it from the battlefield directly into its owner's graveyard. A player can't sacrifice something that isn't a permanent, or something that's a permanent he or she doesn't control. Sacrificing a permanent doesn't destroy it, so regeneration or other effects that replace destruction can't affect this action.
Sometimes-relevant corner cases:
- Tokens disappear when they leave the battlefield, but they still count as going to the graveyard, so you do get Captain triggers.
- Diregraf Captain does "see" any Zombies that die at the same time that it does. So, if you have a Diregraf Captain and two other Zombies on the battlefield, for instance, your opponent will lose 2 life when he kills them all with Day of Judgment.
- If a replacement effect (e.g. Leyline of the Void's ability) makes it so that a Zombie you sacrifice never goes to the graveyard in the first place, the Captain's ability won't trigger.
- "Dies" normally refers to creatures, but if you somehow had a non-creature permanent with the Zombie subtype (like some kind of Zombie Bitterblossom) go to the graveyard, the Captain's trigger would still apply as well.