It is possible it was meant for a CAVE VR room projection system, but I think the more likely answer (as there is no rear view) is that it was just a limitation of the engine. There is no system in Doom for rendering only part of the 2D screen offset from the main view (you cannot pan to look up or down as an example). Doom's FOV was 90 degrees for a single view, so they likely just rotated the drone views 90 degrees to render the "adjacent" area of the screen.
It shouldn't be a limitation to the engine, because they could've either translated to the sides and/or rotated 45 degrees
Speaking of ID games in a CAVE VR... somewhere in late 1990s to early 2000s, I ran into a caveman who was playing with some kind of hacked up Quake for the CAVE. It had integrated the head tracking, so you really got the full-immersion from being able to duck or peek around corners, etc.
I don't remember whether they really made the weapon aiming work with the full 6 DOF wand tracking, or if it was just a walking simulator.
So basically a a real-life 3d skybox, if you're familiar with 3d-engine terms [1]