Just a place to put crack pot theories and the like. I'm not much for rampant speculation but the hype of the boss has made me think something totally absurd up. Or maybe it's not.
1. The Bosses are all different body parts of what may well be a larger entity than it's parts. We've seen the "Maw" and the "Lungs" were mentioned in the stream chat box. The question here is why does what is otherwise a construct need lungs?
2. The Construct needs lungs because it's not wholly inanimate, more chat stuff follows along with this. The Construct parts we've seen are a shell which takes Murk and makes it into muscle mass. This means that The Construct is bio-mechanical and we see evidence of that in the art already. Evangelion was thrown around a little as was Gundam, so The Construct could be thought of as a "Mecha" though that's probably a bit of a reach. This isn't where the rabbit hole ends however.
3. We know the Delver's Drop world is made up of two ancient primordial beings floating on a sea of Murk. There may well be other worlds floating on this sea. We know at least the Cronus Spire sits in a swamp overfilling with Murk and Spoil, the rest of it's condition is unknown but we can at least speculate that it's not in the greatest of conditions.
4. The Construct is obviously large enough to hold people, how many people is hard to gauge not seeing the entire thing all put together but considering how large the Maw is compared to the Delver I'd say quite a few.
Conclusion: The Construct isn't just a mecha in the Gundam/Evangelion sense. It's more closely aligned with Super Dimension Fortress Macross. The Constuct is a "Space Ship", designed to ferry a select group of people to another world, leaving the Delver's Drop world behind.