When the Undead Scourge was defeated nearly definitively at the end of Wrath of the Lich King, this did not mean the end to the threat of the undead. Not only did the Scourge remain an entity, albeit one more or less under control of a Lich King who so far does not seem interested in global domination (though the tactics he uses and encourages within the Knights of the Ebon Blade are questionable at best,) but ghosts and other necromantic horrors have always existed outside of the specific domain of the Scourge. Both the Legion and the servants of the Void have employed necromancy in the past.
While the Scourge was perhaps the most iconic and intimidating terrestrial threat (ok, Old Gods probably take precedence, though I think the Scourge's actions in Icecrown suggest that they had a certain immunity to the power of the Old Gods and thus might have given them a run for their money,) the Legion has, historically, been the greatest cosmic threat (though again, the Void that spawned the Old Gods is likely the greater danger.)
However, under Sargeras, the Legion seemed in a position to really dominate every demon in the cosmos. Demons existed before the Legion, but vast numbers of new ranks were added - we know at the very least that the Man'ari Eredar and the Satyrs were originally members of mortal races (playable ones, in fact) and we could probably assume that a lot of existing demonic races were similarly corrupted specifically by the Burning Legion.
So while we don't seem to be fighting Sargeras directly in Legion (I think he doesn't have a corporeal body to fight,) the datamined dialogue does suggest that the leadership of the Legion will truly be eliminated in one way or another. Kil'jaeden is, I believe, permanently dead at the end of the Tomb of Sargeras raid, and it's possible that Archimonde truly died at the end of Hellfire Citadel (that's tricky, as only mythic kills him within the Twisting Nether, and the cutscene implies that he's back on Draenor when he dies.)
With Sargeras and his two Eredar lieutenants gone, it really does not seem like anyone is in a good position to take up leadership of the Legion. And here's the thing: many of the demons of the Legion were only doing Sargeras' will under threat. I imagine the Eredar and the other "newer" demonic races were devoted to him in a religious way, and would seek to carry on with his Burning Crusade, but beings like the Nathrezim are unlikely to hold any true loyalty to him.
When Sargeras first discovered the Nathrezim, they were serving the Old Gods on a different planet. Given that they are so gifted in duplicity, it would not shock me in the least to discover that the Nathrezim were in fact playing all sides all along. And in the wake of Sargeras' fall, they may eagerly go back to serving the Void.
While Sargeras aligned his demonic forces in opposition to the Void (by way of all of creation,) there's nothing inherently anti-Void in demons.
So basically, after Legion, don't expect demons as a creature type to vanish all together (though they'll certainly take a backseat to things like Aberrations if we're doing Old God stuff next.)