'This place is certainly connected to the realm that Lorien entered. If I'm correct, it might have even grown from the layered Dungeons, or be the reason the layered Dungeons appeared in the first place…'
The details almost didn't matter right now, though. What was important was what the D-Grade Thryskai Feather was capable of.
Because of its existence, Sylas was able to use the obelisks. Essentially, the feather was like a domain of its own, capable of allowing Aether to gather properly and trigger the hidden effects of the obelisk.
By extension, then, it was obvious what the Thryskai would want to use it for. They wanted a chance at disrupting this quasi-system with a domain of their own. The hope was that by disrupting the system, they could have a chance to enter personally and take advantage of whatever was here.