Probably uses a swap file on the 8MB of flash which most likely has just as fast read speeds as the original Dos PC's ram did.

*Edit*

it looks like it is using a clone of Doom called PrBoom so the system requirements of the original would not apply. Kind of misleading but my eyes are so bad I probably couldn't tell the difference between Doom or Pong on a 1.3" screen anyways!!!