While I'm back east, I've been more or less WoW-less (my laptop was new during Wrath of the Lich King, and makes Legion content kind of slow - and I'm definitely feeling that MMO FOMO effect, and thus limiting my visits to Blizzard Watch and MMO-Champion.) But it has given me a lot of time to work on my D&D campaign (one of our party members is also out of town for an extended period, so this would be downtime anyway.)
My D&D setting is wholly original (to the extent that anything is truly original) because making up fantasy worlds is basically my life's calling, but I couldn't deny the influence that Blizzard's flagship universe has had on my own tastes, and while it might have begun its life as a Warhammer clone, the amount of work that the creative folks at Blizzard have put in to making Azeroth (and the larger Warcraft universe) dense and interesting has made for one of my favorite fictional settings.
D&D, largely due to its pencil-and-paper system and a human dungeon master, is a game that is pretty easily modifiable. They do have their own standard setting in the Forgotten Realms (as well as some other settings like Greyhawk, Ebberon, and Dark Sun,) but the Dungeon Master's Guide has a pretty sizable portion of its text dedicated to ensuring that those who want to build their own setting have plenty of tools to do so.
Apparently, long before I started playing D&D (which was only like... a year and a half ago or something?) and possibly before I started playing WoW (which was ten and a half years ago,) there was actually an officially supported Warcraft D&D module. I believe it spun off to become its own RPG, but then was canceled and even declared officially "non-canon unless we say otherwise" much like the Star Wars Expanded Universe (goodbye, Jacen, Jaina, and Anakin Solo! Though Grand Admiral Thrawn has apparently been salvaged.)
Anyway, whenever that RPG ended, I think we've seen a lot of things in WoW change. The Chronicle books have gone to huge lengths to put together a comprehensive canon in a way that never really existed before.
So, I love the Warcraft setting, and would find it a lot of fun to play a D&D game set in it (though probably not as DM, as I think any games I DM would probably be in my own setting(s.) How would we go about translating the game?
And to be clear, this is basing all of this off of 5th Edition rules, which is the only version of D&D I'm familiar with.
A lot of races would translate easily. D&D does a lot of sub-races, and so while in WoW, Night Elves and Blood Elves might as well be entirely different from a gameplay perspective, you could easily make them into sub races of the broader Elves in a D&D setting (and this would make it simpler to add High Elves, Nightborne or Highborne as additional sub races.) Likewise, you could use this to distinguish out the three major dwarf clans (even adding the Frostborn - remember them?)
WoW races tend to go a little broader, especially as you get the added ones and the Horde ones (though Volo's Guide to Monsters adds some more outside-the-box races.) There could be some questions about what exactly constitutes a sub-race. For instance, Trolls are pretty diverse on Azeroth, and so you could imagine making sub-races for Drakkari, Farraki, Gurubashi, and Amani trolls (Darkspear count, I believe, as Gurubashi, as their original homeland was Stranglethorn Vale.) But when it comes to Orcs or Tauren, it's not totally clear to me whether the different clans and tribes would count as totally different sub-races or just kind of cultural differences that wouldn't really count except for RP purposes. (And that's also setting aside the issue that I think the canon is that most Orcs basically stopped caring which clan they were from when the Horde joined - and there's probably a lot of mixed-heritage Orcs these days.)
A fair number of races would probably have to be made whole-cloth unless you really wanted to stretch things. Would Draenei simply use the stats of the Aasimar? They're both very light-based, even if their backstories and looks are pretty different. Another interesting issue is that of Worgen and Undead. In both of these cases, the "race" is really just human, and so you'd have to figure out how the other effects interact. In WoW, they decided to make Undead count as humanoid and not speak Common for balance and gameplay purposes, but in D&D, having everything tightly balanced is not really as important as making for a good story. So giving Forsaken characters the "undead nature" effect that many monsters have would make lots of sense. You'd also have to see if the effect of Lycanthropes in D&D would have to have some other effect given that the Worgen curse is a little more specific and harder for other people to catch than standard werewolfism.
One of the benefits of doing Warcraft as a tabletop is that you could more easily add in other playable races. Having Ogre, Vrykul, Furbolgs (which are pretty different than D&D Firbolgs) and Naga are easier to fit in when you don't need to worry about the knife-edge balancing we expect for the computer game (and you don't always need to worry about making an equal number of Horde and Alliance races - hell, you could even do buddy-cop stories where the party is of mixed Alliance/Horde make-up.)
Like races, there are a lot of direct-translations between the classes in WoW and those of D&D. Paladins are Paladins, Druids are Druids, Rogues are Rogues, Warlocks are Warlocks. Monks are Monks. Rangers, Fighters, and Wizards work out as pretty clear analogues of Hunters, Warriors, and Mages. On the other hand, D&D has a few classes that would probably fall under another class's domain in WoW, like Sorcerers (which is like a Mage who got power from raw talent rather than years of study) and Barbarians (where are like Warriors who are more primal and spiritual.)
WoW, on the other hand, has a couple classes that are pretty unlike anything you find elsewhere. Death Knights could maybe-kinda use the Blackguard (which is only found in D&D's Unearthed Arcana blog) or Oathbreaker Paladin oaths, but one sort of feels like it should be its own thing. And if Death Knights do sort of have precedence in other fantasy stories (like the Nazgul in Lord of the Rings. I'd call those guys Death Knights) Demon Hunters really feel pretty unlike anything I've seen anywhere else, and you'd probably want to just create a whole new class for that.
Then you'd also have to ask if you wanted to kind of orient classes more around their WoW specializations or keep the D&D variants. For example, Warlocks in D&D can have different sources of magical power - from the standard Demonic/Devilish (in D&D there's a distinction) Fiend, to the Archfey (anything from a Faerie being that would probably be someone like Cenarius or Goldrinn in WoW) to a Great Old One (which in WoW would basically have to be an Old God or at least some high-level C'thraaxi or N'raqi.)
Though to be honest, D&D generally gives players more options to vary their classes. Priests can choose from a wide variety of domains (based on the god or principle they worship) and Wizards can specialize in several different schools of magic (but are not typically stuck to one element or the other.) For a lot of WoW classes, the specializations don't have all that much to do with flavor as much as they do with mechanics, but some are a big deal (like Holy versus Shadow Priest.)
Either way, D&D classes don't really have anything like tanking, and everyone has to be a little more self-sufficient given that you can't really play a class as "the one who never gets hit by anything" which is like, most WoW characters.
Monsters and Dungeons:
Dungeons are, in a way, the easy part. WoW has a huge number of dungeons that you could use as inspiration, or you could turn any number of memorable questing zones into dungeons, or just make stuff up.
Of course, it wouldn't really be a 1 to 1 translation, as a computer game can generally handle combat very easily and quickly and handle character interactions less easily. But imagine a version of Deadmines where you sneak into the place disguised as bandits, maybe try to convince one of the bosses to let you get through to the ship, and then have a climactic fight with Vanessa at the end. D&D certainly lets you have exciting combat encounters, but it provides a whole lot more freedom to either avoid combat or seek other outcomes (actually, forget that climactic fight with Vanessa. Imagine instead convincing her to denounce violence and reform the Defias into a political advocacy organization.)
Like a lot of D&D modules (there have been a number of ones based on Magic: The Gathering settings, which is my first deeply nerdy love,) you could simply use "close enough" creatures from the Monster Manual to remake iconic Warcraft creatures. Kua-Toa are almost exactly Murlocs, but you could also translate something like Modrons into various Titan creations like Mechagnomes.
Of course you could easily come up with new threats for players to deal with. There's plenty of stuff to choose from. Alternatively, you could kind of remake some of the WoW expansions as campaigns.
Of course, WoW's level cap keeps going up and D&D is set up to go from 1-20, which makes each level a lot more significant. But for a long time now, level in WoW has been a purely mechanical thing. I don't think anyone would argue that Blackhand, even with all his Iron Horde tech, was truly more powerful than the Lich King. So it wouldn't be hard to simply start new campaigns as "new adventurers coming off the boat in Northrend."
But the freedom of D&D would also let you do stuff that WoW is unlikely to ever do - like having players fight their way through a post-Arthas Northrend.
Ultimately, D&D and its variants can be used to play through most fantasy settings. And given that WoW is one of the most popular RPGs that owes a big debt to the quintessential one, it might be a fun project for anyone involved to create a campaign that has you adventure across Azeroth.
And it's probably the only way you're ever going to play that Tauren Bard you always wanted to play.