Slepnir is also a resident of Eureka in FFIII but oddly is not paired with Odin.
In Final Fantasy Tactics, Eureka is mentioned as being a "Wonder" that is destroyed in The Cataclysm and was home to an ancient royal family called the Kashka dynasty. I've never heard of that before. Of course, it also says that the Crystal Tower had something to do with Baron from IV and has a labyrinth at its base. We find out later from IV that the King of Baron turns out to
Odin. Some relation to his appearance now?
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In the video that briefly shows the tower, I don't see a labyrinth. But if it existed in FFIII universe it wouldn't make sense that it would exist in FFXIV's since well... since I believe that we're on the other side of the door. But if there as an Ancients maze that would throw a huge monkey wrench into my theory that Eorzea is actually the forbidden land of Eureka.
Or I could explain it by saying that Louisoux somehow brought the labyrinth to lock Bahamut in it.
Back to the Tactics mention of Eureka: Not much is known about the Cataclysm. It occurred in Ivalice at some point after the events in FFXII according to FF Wiki. But when the Cataclysm occured really isn't nearly as important as the fact that there was a possible link between Eorzea (IF it is Eureka) and Ivalice of XII and Tactics. According to the Wiki, The Cataclysm supposedly destroyed all Moogles. In FFXIV, the Moogle King was disturbed by a big war and decided to lower his subjects via a long rope to the promised land, but remained stuck himself. The Moogles, through this legend, admit that they are not natives of Eorzea but come from "the land of the gods". While I had always assumed that this was some fanciful Far Far Away, it is actually fitting for it to be Ivalice, since the "gods", the Occuria, were involved in a war that that threatened to destroy everything, and apparently eventually did.
What seems to me, to be honest, is that once the key of Eureka was used, it created a portal that apparently never shut, allowing people to travel freely and rather randomly (*cough*Lightning*cough*) into our universe. I don't think Eureka was destroyed in the Cataclysm of Ivalice but the portal to Eureka was.
So that's my current theory. I'm looking to figure out what is the actual reality in a few weeks. :3