This is an ancient dwelling that was build under the rim at Montezuma's Well, which was a major water source in the desert there.
Montezuma's Well is a huge cavity in the gound with an underground water supply at the bottom, and these steps lead down to the bottom. The sign down there warns visitors to stay on the trail.
This dwelling is near the bottom of Montezuma's Well. It is much cooler here than it is at that other dwelling near the rim.