Yume Kōjō: Doki Doki Panic (1987) by Nintendo Famicom Disk System game
Doki Doki panic ROM? : r/Roms
Doki Doki Panic - Gameplay on Original Hardware (Famicom Disk System) - YouTube
Found an NES version of Doki Doki Panic on eBay! Thought it'd be a hack of the original sprites on top of Mario 2 but this appears to be the original game!