All Player Character Races use one skeleton. Allied Races included.
The Zandalari and Nightborn do not use "The Nelf Skeleton" and the Dark Iron Dwarves don't use "The Dwarf Skeleton".
They all use the exact same single skeleton as Worgen and Goblins.
Yeah. I know. CRAZY. But lemme show you how it works!
Back in Cataclysm the Developers started working with an Adaptive Animation Model. That is, a rig or skeleton which can animate different parts independently of one another, and which can be stretched or altered in shape while still retaining functionality. This Skeleton was shared between Goblins and Worgen, though you wouldn't know it by looking at them.
When MoP came along, the Developers had to create monk-specific class animations for every race, which was -super- time consuming and kind of highlighted how damned hard it is to make new classes while adding new races to the game every other expansion. The Worgen and Goblin were excluded from the animation-batching because of how much time it would take to put all of those animations on yet another skeleton.
When WoD came out, however, with it's newly remodeled races, it wasn't just some random decision to make PCs look better: The Developers and Producers had decided to shrink their overall animation workload going forward by moving all races to the new Unified Player Skeleton. It took -boatloads- of work but it had to be done because you couldn't just slap the old models onto the new skeleton and have it work correctly, you needed to make models that specifically anchored to the appropriate points on the new skeleton.
This is also why Goblins and Worgen didn't get model updates: They didn't -need- them. They could use them, sure, since they look kinda bad compared to the rest of the races, but their re-design wasn't needed to move forward with the Unified Player Skeleton since they were already on it.
Then, with Legion's "Class Fantasy" focus, the Developers -further- lowered the need to design every new race's specific combat animations for the different class attacks and spells. Using the single skeleton and adaptive animation design, they created one "Charge" animation that all warriors share, regardless of race. One "Mongoose Bite". One everything. The amount of animation workload required to add even a single new race is now -massively- lower.
This is why when you have a Worgen in the WoWhead model viewer you can view the Monk animations. This is why when you're playing a Demon Hunter in Court of Stars and get transformed into a Nightborn (Which did use the old Nelf Skeleton) the model got stuck whenever you used Blade Dance even though the "New" nelf can use Blade Dance.
This is also why Nightborn had to be remodeled for Players to use. Because they're using the new Unified Player Skeleton. And yeah, they're currently using the Nelf Animations. But they don't -have- to.
Check out this Sethrak from Battle for Azeroth.
Notice anything about their weapon attacks? Those are Pandaren Male attacks, but that is clearly not the Pandaren Male "Skeleton".
Notice anything about their walk animation? That's the Worgen Female walk, but that is clearly not the Worgen Female "Skeleton".
It even uses the Pandaren Male Generic Casting animations! (Which will soon be depreciated outside of things like casting your Hearthstone or other non-class-specific spells)
This is because all three models (Pandaren Male, Worgen Female, Sethrak) use the same Unified Skeleton.
Blizzard now has the ability to mix and match animations pretty much at will. In any direction or order they like. They can make new races without having to spend weeks re-animating the class-attacks and class-spells. Even the new Caster Pose Animations are meant to offset the issue. Go load up a Void Elf Female in WoWhead's modelviewer and do the Shaman and Druid casting animations (she looks kinda great doing them!).
This stuff could be the basis of a massive explosion of new potential player races because the effort required to put them into the game as NPCs can be directly turned around and made into the effort required to make them into playable races without having to go back to the drawing board for a redesign. It's also the best chance we have at a Dance Studio option, since they can now make a single new dance emote and allow any race to use it.
And if that's not the coolest shit coming out of WoW, lately, I dunno what is.