How are the walls designed to force the narrator into the pit?
The walls of the narrator's prison are not attached to the floor or ceiling. That means that the walls themselves can move independently from the rest of the room.
It proceeded from a fissure, about half an inch in width, extending entirely around the prison at the base of the walls, which thus appeared, and were, completely separated from the floor.
The walls can be slid toward each other. If you saw the original Star Wars that should make sense. Luke, Han, Leia, and Chewy are all in the trash room, and the walls begin closing in on them. That's the same thing in Poe's story. Except the middle of the room has a really deep pit. The walls themselves move a bit differently too. They change angle and make the room take on the shape of a pill or "lozenge."
In an instant the apartment had shifted its form into that of a lozenge.
The narrator could choose to get crushed by the walls or jump into the pit. But getting crushed by the walls is an almost impossibility because the walls are made of iron and are being heated. They would sear and burn him badly before they crushed him. The entire point of burning hot walls that are squeezing in on the narrator is to force him to jump into the pit.
Amid the thought of the fiery destruction that impended, the idea of the coolness of the well came over my soul like balm. I rushed to its deadly brink. I threw my straining vision below.