The way Build mirrors work is to copy the level geometry across the mirror plane. Recursion or moving the mirror would not be possible.
Arbitrarily placed, see-through, traversable, Portal-style portals probably would not have been beyond the skill of the engine implementers. But to make them work smoothly, along with everything else in the game, under the constraints of the hardware on which the game had to run? I find it hard to imagine anyone being able to pull that off, tbh.
You might be able to subdivide the build engine's sectors into visleaves (borrowing terminology from Source) and clip all sectors in the mirror-verse according to the aperture + view-frustrum. To work correctly you'd need to do this every frame, probably an unthinkably huge task for the hardware at the time.
If you can lie to the engine and say that the flipped/portal camera is still inside the sector that the player is in (even if that's clearly wrong by the camera coords) then maybe your engine culls walls/floors/sprites not visible and you don't need to reserve an empty void for the mirror/portal camera to render from, so that level geometry can occupy the back side and make the illusion convincing.