The article touches on this, but for them unfamiliar, the quake .map format is the editable text based format. but it does not use the common method of vertices into edges into faces as the base building block. it uses planes, the graphics primitive is is the three points that define a plane, where these planes intersect are the edges.
I never dove into the subject enough to figure out if this plane representation was also internal to the compiled bsp format, but I suspect it is. My guess is that it is the natural conclusion when you need a map interchange format for your highly optimized space partitioned engine.