You just asked this on the "Cool Spot (SNES)" forum. At least give someone there a chance to reply. Here in the general forums we don't know details on specific games.

(Unrelated: For years I searched for the name of this game, because I played the demo as a kid. So thank you for that :) )

No no no. You were supposed to ask there and not here. The runners/moderators of Cool Spot (SNES) know better about the game than we in the general forums. Also, wikipedia says that the game was developed for the SNES as well as other platforms, so maybe a specific version for NES does not exist.