The left was outside, the mountain face was basically a vertical line, and all the things we associate with "deeper" were found further and further to the right of that line. Some ways in you'd find an underground river (which floods when you first find it), then a chasm (enemies spawn from here), then a magma river, [spoilers for ancient versions of DF start now] eerie glowing pits, and finally adamantine. Finding adamantine made the king show up and demand you mine more and more adamantine, but the more you mined the more likely you were to have your fortress suddenly end in a cutscene.
All these fixed elements gave the game a specific progression of increasing rewards and challenges, and a guaranteed story arc for the whole fortress.
From what I've seen, it was fully 2-D: the "surface" was to the left, then you hit the mountain face, and the further to the right you went, the deeper you were, until eventually you breached the proverbial Hidden Fun Stuff.
