The entire world is in the grip of a computer known simply as The Big One. Its code is far too complex for you to crack, so you must find scientists, drug them, and bring them to The Big One. Each will be able to unlock one letter. Simply finding these scientists is the hard part - The Big One has aliens patrolling its base, and they are more than capable of ganging up on you.
In essence Parallax is a top-view multi-directional-scrolling shoot 'em up. Improved weaponry and shield recharges can be bought by the machine - can you think of a way to get money from a drugged scientist? You can duck under the layers of surface, but so can the aliens, so action can take place here. You can also get out of your ship and patrol the area on foot.
The game's parallax scrolling routine inspired the title, and it also has 11-minute introductory music.