That was the first FPS game I played, and it appears to use a very limited form of raycasting. Maybe just drawing entire walls with one raycast and some scaling.
It looks like "pop-in" happens frequently on that so I'd wager that a short ray and not very many to create a whole circle (which would necessitate only looking at closer things) meant a ton less calcs per frame.
That was the first FPS game I played, and it appears to use a very limited form of raycasting. Maybe just drawing entire walls with one raycast and some scaling.