Arthur J. Hackensack, an insane Texas billionaire bent on conquering the world, kidnaps professor Frobisher Goonhilly, a paranormal scientist working on a matter transformation weapon. As a demonstration of its powers, Arthur transforms the Isle of White into a giant custard slice, New York into a bath sponge and the Eiffel Tower into a toast rack. The ghost Blinky, secret agent for S.P.E.C.T.R.E. (Society for the Prevention of Ectoplasmic Crime, Telekinetic misuse and Reality Endangerment), infiltrates the madman's sea ship (the newly raised SS Titanic) armed with an ectoplasmic gun and a case full of disguises.

Titanic Blinky is a platform game similar to Dizzy, replacing the egg protagonist with a slightly effeminate ghost. As in that game, the aim is to collect objects to solve puzzles. One main difference from Dizzy is the fact that Blinky carries a gun with infinite ammunition. There's an energy bar at the bottom of the screen that gets depleted every time Blinky touches an enemy. When it is empty, Blinky literally flips over and the player loses one life. The game starts with three lives, and there is no form of saving progress.