Really? I was under the impression that Wolfenstein pre-rendered the wall tiles and then simply scaled everything. /me considers looking at the code.
I think it's a pretty basic raycaster, where 1-pixel wide columns are rendered. You cast out you ray and a vertical strip of texels from the appropriate position along the first wall it hits is rendered. There's no floor or ceiling texturing so large rooms are a bonus since most of the columns are going to be far away and thus short and not have many pixels to calculate. It's a strategy that would work well* with software MIP mapping, since the far away walls will tend to skip a lot of texels on the standard sized texture and thus be cache-inefficient.
*also one which would work well if the wall textures are actually rotated 90 degrees so that the vertical scan "down" the wall texture is, in reality, a linear scan through the texels "horizontally"...
Presumably something like this is used, if it wasn't, it is a real waste, especially on any system with a data cache.