How Magical Chase does it is pretty simple, and any game can have the same effect; the sections of the background in Stage 3 of Magical Chase are just unbroken horizontal bars (sky, clouds, a wooden floor and ceiling) -- these can be moved around at will just like the sections of a slide rule. The wooden stumps, turrets, rivets, etc that poke out from the floor and ceiling are sprites. It's the same technique that is done on countless other shmups.