This alarm clock would use the same technology found in Nintendo’s old Game & Watch handhelds, which had an LCD display with a color background layer. This would allow for a display comparable to the original Game Boy Color, and enable a simple alarm animation (which was another staple of the Game & Watch devices).
The animation would go something like the following. None of the animated elements can overlap, which is why it looks so simple.
Of course this alarm clock would play music from the game, which had an amazing soundtrack. The over-sized cartridge on the top functions as a snooze button.
I believe other games could get a similar treatment. The ending of Super Mario Bros. 2, for instance.