[Neomi]

Minor spoilers, probably...
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I think finishing the chess game effectively blocks off all possibility of finishing that floor (unless you can still go all the way back down after Islanne teleports you to the surface, but I don't think that works). Once you defeat the ice, fire, slime, and air rooms you automatically jump to the chess game. I usually try to clear the entire level and rest before meeting the last of the four foes.

To answer your question about exploring the rest of the level, if you haven't cleared the cave area you missed out on a few tough fights with undead and a small cache of treasure. If you haven't explored the area with the statues you missed a few good battles with wyrvens and such. If you didn't explore the area with a bunch of bridges, you just missed some skeletal archers and piles and piles of magic arrows... Nothing that was absolutely necessary, just more loot.

I think I'm remembering that level correctly, someone please correct me if I'm wrong (it's been a few months since I ran through Durlag's Tower).