Kul Tiras is probably doing fine, honestly, since we headed off the disasters that would affect their population before they really happened. Stormwind, in spite of being a backbone nation in the Alliance militarily, hasn’t had a major disaster happen in its homelands since the First and Second War, barring a few pre-patch events where Stormwind City was attacked. Kul Tiras and Stormwind are probably pretty equal in population and pretty well-off comparatively, especially since the latter was more than likely heavily bolstered by refugees from Lordaeron and other defunct human kingdoms.
The Three Hammers, ergo the united dwarves clans, are extremely well-off right now, and are the de-facto top dog nation in terms of both factions. While the Wildhammers did have some serious setbacks in both Cataclysm and then Legion, wherein the Highlands were overrun twice. Other than that, the dwarf clans haven’t suffered a major disaster on their lands in 300 years, since the War of Three Hammers, and could basically roll over anyone if they chose.
Orcs as well are, to be blunt, very good at multiplying, which was mitigated only by their originally harsh lifestyle. Barrens and Durotar are comparatively a walk in the park compared to the native habitat of orcs, who are considered adults, and fully grown, by age twelve (contrasted with humans who aren’t considered truly done growing and developing until their early twenties). This essentially means that an orc who was born in the camps could be a grandparent already. While the Siege of Orgrimmar seemed dire for orcs in general, it was later stated that ‘only a small number of orcs’ actually supported Garrosh, so in general they’re doing just fine.
Goblins, same deal, they’re doing pretty good for themselves, especially since they’re literally only separated via different cartels, and can swap whenever they please.
In contrast, gnomes are probably in dire straits to an extent. The Fall of Gnomeregan is often glossed over by Blizzard, but per lore it was an event on par with the Fall of Lordaeron to the Scourge, with a massive loss of life.
Most of the other Horde races are probably at least doing okay. In terms of Elves, ironically the Nightborne are probably doing the best of all of them, unlike the night elves they don’t seem to have any trouble with population growth, given the sheer number of outcasts we see on the Broken Isles, and yet Suramar itself was still very densely populated. Night elves took a fairly grievous hit, of course, but I don’t think they’re in danger of going extinct, though they’re not doing all that well.
Draenei apparently took one for the team during Argus and are militarily defunct, but they never had a large military so it might not be a huge issue with population.