According to the manual of Escape from Singe's Castle, as soon as Dirk the Daring saved Princess Daphne from Singe, the Shapeshifter teleported her away. It appeared to Dirk, saying that Daphne was the bride of the wizard who owns the castle.
In the end of the game, Dirk reaches "The Shapeshifter's Den" where Daphne is laid on a stone table. The Shapeshifter appears, as a floating cloaked featureless figure with pointed hood, carrying a halberd, hurling thunders towards Dirk. Dirk eventually kills it by throwing his sword at it.
A figure similar to the Shapeshifter appears in the episode "The Legend Of The Giant's Name", a floating cloak armed with a wooden club, but the superficial similarities might be just a coincidence. It's possible however that the that episode was an inspiration for the game designers.