Keep in mind, I am not a programmer.

The only thing from the original game being used here is the original WAD files to create the levels in a custom engine. The Doom engine is not being used here (it is not usesd in most "ports" of Doom). Most of the ports of Doom that are celebrated are actually not running on the original item featured. Such as the pregnancy test one - they removed the original CPU, screen, pretty much all electronics inside were replaced to make that "port" possible.

The Atari 2600 port doesn't use anything from Doom other than the name as far as I know.

At least with this Neo Geo work in progress, they are using the original WAD files, something most ports cannot claim.

I believe the engine is raycasting along the lines of Jurassic Park's 3D interior scenes on the Super Nintendo. At the end of the day, the graphics are still limited by what the platform can push. The Neo Geo was not designed with 3D like this in mind at all.