This page explains in detail the interactions between the Donkey Kong series and the Gremlins series.
Gremlins[]
June 8, 1984
Donkey Kong
Gremlins
In the second scene showing the new batch of Gremlins, Stripe can be seen playing the Coleco Donkey Kong Tabletop LCD. Oddly, it has an additional Donkey Kong Junior sticker on its back. This was done likely because of the game resulting too bland without anything on it, as it was going to be shown from its back.
License[]
The creators of Gremlins didn't held any right over Nintendo's Donkey Kong, but they've only shown the game for a brief time.