We know from the Sermons and our Hunt for the Amaranth that the Numidium is a walking way, a way to achieve divinity or to break the rules of the Aurbis in some other form. The Loveletter from the Fifth Era indicates this clearly.
We also speculate that the account of Vivec in his 36 Lessons are supposed to be mythical, but our Hunt for the Amaranth would have us believe that the events in the 36 Lessons did indeed happen. How? The striking of Lorkhan's Heart caused a Dragon Break or some other localized time distortion. Within these events, ALMSIVI as a divine oversoul of Vivec, Almalexia, and Sotha Sil attains apotheosis. Gods in the Elder Scrolls universe have to have always existed, and so the universe had to mend itself to the new divinity ALMSIVI.
My personal theory as to what happened to the Dwemer comes from a literal interpretation of Sermon 36. During the time distortion/alternate universe-thingamahjig caused by the use of the Heart by Kagrenac, or possibly the Tribunal to attain divinity, the forces of Resdayn (Chimer) fought the forces of the Dwemer.
Here is what happened to them. I suggest you read the full http://www.imperial-library.info/content/thirty-six-lessons-vivec-sermon-thirty-sixfor the full context.
Red Mountain exploded as the Hortator went too far inside, seeking the Sharmat.
Dwemeri high priest Kagrenac then revealed that which he had built in the image of Vivec. It was a walking star, which burnt the armies of the Triune and destroyed the heartland of Veloth, creating the Inner Sea.
Each of the aspects of the ALMSIVI then rose up together, combining as one, and showed the world the sixth path. Ayem took from the star its fire, Seht took from it its mystery, and Vehk took from it its feet, which had been constructed before the gift of Molag Bal and destroyed in the manner of truth: by a great hammering. When the soul of the Dwemer could walk no more, they were removed from this world.
Resdaynia was no more. It had been redeemed of all the iniquities of the foolish. The ALMSIVI drew nets from the Beginning Place and captured the ash of Red Mountain, which they knew was the Blight of the Dwemer and that would serve only to infect the whole of the middle world, and ate it. ALTADOON DUNMERI!
Dwemeri high priest Kagrenac then revealed that which he had built in the image of Vivec. It was a walking star, which burnt the armies of the Triune and destroyed the heartland of Veloth, creating the Inner Sea.
Each of the aspects of the ALMSIVI then rose up together, combining as one, and showed the world the sixth path. Ayem took from the star its fire, Seht took from it its mystery, and Vehk took from it its feet, which had been constructed before the gift of Molag Bal and destroyed in the manner of truth: by a great hammering. When the soul of the Dwemer could walk no more, they were removed from this world.
Resdaynia was no more. It had been redeemed of all the iniquities of the foolish. The ALMSIVI drew nets from the Beginning Place and captured the ash of Red Mountain, which they knew was the Blight of the Dwemer and that would serve only to infect the whole of the middle world, and ate it. ALTADOON DUNMERI!
This sermon's events are so out of tune with what the actual in-game account of the battle presents that it can't be merely metaphorical. In the "real" timeline, we know that the Dwemer never used Numidium in war. We have zero indication that the Inner Sea was created from such use. We can assume that the Inner Sea had existed since Nirn for that matter.
ALMSIVI, in this sermon, somehow combines and stops Numidium for destroying Veloth, and the whole of Resdayn from that matter. Here is the biggest clue of the real disappearance of the Dwemer: When the soul of the Dwemer could walk no more, they were removed from this world.
Our Hunt for the Amaranth tells us that the walking ways are ways in which to achieve divinity, CHIM, or perhaps even the state of Amaranth itself. Vivec in his sermons notes that the Dwemer lacked any concept or notion of love, yet they attempted a walking way, that of combining their race as an oversoul into an artificial god - Numidium. When they could walk no more, possibly due to their lack of love (which we know to be critical in striving for/attaining Amaranth and/or CHIM).
The biggest note of curiosity is how this sermon describes The Blight.
Resdaynia was no more. It had been redeemed of all the iniquities of the foolish. The ALMSIVI drew nets from the Beginning Place and captured the ash of Red Mountain, which they knew was the Blight of the Dwemer and that would serve only to infect the whole of the middle world, and ate it. ALTADOON DUNMERI!
The Beginning Place, according to http://www.uesp.net/wiki/Morrowind:Varieties_of_Faith..., is where Akatosh first formed and allowed other spirits to assume form in an easier manner. ALMSIVI "drew nets" from this place to catch the Blight of the Dwemer which they claimed would consume the whole of the Middle World (normal timeline, maybe). Then they ate it.
What happens right after they eat the Blight of the Dwemer? ALTADOON DUNMERI shows up as the third last phrase of the Lessons. This is important because ALTADOON means weapon and DUNMERI obviously means Dunmer, Dark Elves. Dunmer was never used throughout the course of the sermons, as in their timeline Vivec is leading the Chimer people.
When ALMSIVI eats the blight, the Dunmeri are born. Common in-game lore would have you believe that Azura cursed the Chimer for following the Tribunal by turning their skin dark, but that is how normal timeline mortals view it. When the Tribunal achieved apotheosis, then by the rules of the Aurbis they would have had to have always been gods from the beginning of time, and this is how the Aurbis managed to mold them back into the normal timeline.
Maybe the Inner Sea never existed before the Battle of Red Mountain, but when all these events happened, the Inner Sea had always existed. No one can question it because no one is exempt from the time-mending rules of the Aurbis.
So, my theory: The Dwemer disappeared because ALMSIVI ate their Blight and wiped them from the face of the universe. Their Blight was their amoral quest for godhood without having the slightest concept of love or what it means to love. They are kind of like a corrupted CHIM or a corrupted Amaranth. If Amaranth requires love to attain, then the opposite of Amaranth would require not having a concept of love.
Even if this was all Tribunal mumbo-jumbo propaganda, that doesn't explain why this sermon attributes the Blight to the Dwemer and not to Dagoth Ur, if by normal in-game lore we are led to believe that Dagoth Ur is the single, solitary source of the Blight and that this Blight didn't start spreading until he reemerged into the Heart chamber some centuries after the battle.