Description taken from Arcade version of this game

In Gorf you control an Interstellar Space Fighter that maneuvers in all directions around the bottom section of the screen through five stages of outer space shoot-em-up action. Your mission is to keep Gorf's fleet of robot ships from conquering the galaxy.

The first mission, called Astro Battle, looks and plays a lot like Space Invaders. In this mission, you must shoot descending rows of aliens while hiding behind a thin arch-like shield which stretches across the screen. The next stage is called Laser Attack. In this stage, robot ships, laser ships and Gorf robots fly and dive at you, shooting laser bursts. You must avoid enemy fire while shooting back.

The next mission is called Galaxians. Not surprisingly, it plays a lot like Galaxian. The Space Warp is next in line. In this stage, you must shoot Gorfs and Space Warp Fighters as they spiral out of a tunnel-like warp in space.

In the last mission, the Gorfian Flagship flies back and forth across the top of the screen, shooting fireballs towards your fighter. You must clear a hole in the ship's electromagnetic field and then explode its internal power reactor vent, which is the pink section in the center of the ship. When you complete the fifth stage, the action intensifies, and you must repeat the process again and again. At certain points during the game, an unseen alien narrator comments on the action. ~ Brett Alan Weiss, All Game Guide