Many people seem to consider them undead, but unlike the Undead they have many physical features/abilities that is very much something you would find among the living. The big one is blood flow.
Someone once asked Blizzard if Arthas could get it up after he had been DK-ified. Whether it was a joke answer or not, Blizzard replied that he could. Well to ‘get it up’, you need to have blood pressure and blood pressure means you have a heartbeat and blood flow. The undead do not have a heartbeat.
The DK also has frosted breath. If you look at any animation of them, you’ll notice they are actually breathing. The undead do not breath.
The Death Knight also does not seem to react to the Light in the same way that the undead do. It seems to only weaken their power and not really harm them physically any more than it does to the Living. The Battle for Light’s Hope is a clear indication of this, as is Sir Zeliek who wields the Light instead of the Shadow magic he was imbued with.
The Undead, however, fear it and are burned by it with the exception of the playable race. Though even they are probably harmed by it and just simply replace their body parts after a while. Honestly the Undead race shouldn’t have holy priests imo, but that is another topic.
Death Knights are also classified as Humanoid in game, whereas similar ‘humanoid’ undead are simply classified as Undead.
Death Knights also cannot be turned by Paladins, and not because the game mechanics won’t allow it, but simply because they are not undead. In game and in the stories, no paladin has tried to turn a Death Knight.
So what are they? Are they really Undead or are they simply mutated, resurrected heroes similar to how the Orcs were mutated by Mannaroth’s blood? I would say the latter if you go by the Death Knight starter quests.
The fallen hero had been slain by the Scourge, experimented on and resurrected back to life rather than simply reanimated with a consciousness like most undead are. They were given necromantic powers over life and death, and the undead, and their memory of their previous life pretty much wiped.
The memory wipe would explain their loyalty to Arthas. They know nothing else. It is until the Death Knight is exposed to someone they knew, that they begin to remember who they once were and Arthas’ influence begins to weaken.
The Shadow also naturally does not want to bring dead things back to life, and some of the Initiates do not survive the transformation and are either driven mad by the magic, remember something of their past or from hearing Arthas in their head.
In conclusion Death Knights are very much alive. They are resurrected heroes who become necromancers in plate armor. The process that brings them back to life is what allows Arthas to psychically communicate with them and alters their physical appearance. They are not Undead or Lichs in armor. They are the Living that has been stripped of their identity and mutated by Shadow magic.
There’s a bit of confusion between game mechanics and lore. Player Death Knights are classified as “humanoid” the same way as undead players are. Apparently undead players were at one time classified as Undead, but this cause a number of mechanics issues and was changed long before the game came out of beta.
If you look at the NPC death knights, (such as the ones in Acherus) they’re properly classified as undead:
The breathing is also a game mechanic. Death knights don’t use separate models in the game, they use the same model w/ an effect for the eyes, and extra textures for the undead customizations. Even the undead models have breathing animations.
EDIT:
For game balance, the Forsaken are registered as humanoids because, in a PvP setting, they would be massacred with [Exorcism], [Holy Wrath], [Turn Evil], and [Shackle Undead], but they would also be immune to other CC such as [Polymorph] and [Fear].
Forsaken were classified as undead in Beta, but it proved to be too
problematic with PvP balance. Many Forsaken NPCs are also considered
humanoid.