The game is cheating a little bit, since it loads a lot of read-only data from external SPI flash memory, and all the code is in the internal 1MB flash. On your 386, everything including the OS had to fit on that 4MB RAM.

It also doesn't have quite all the features. No music, and no screen wipe effect (I worked on a memory constrained Doom port myself, and that silly little effect is incredibly memory intensive since you need two full copies of the frame buffer)