The Addams family are not very strange, in fact they are quite smart. You see, it was Ma-Ma who always warned of the alien UFO coming to invade their city. All the other Addams thought she was crazy, but Ma-Ma, using her crystal ball, put a protective spell on the Addams family house.
As Uncle Fester was Moonbathing one night, the fabled UFO appeared and beamed all the people in the town up. When the Aliens scanned the Addams house for life forms, they found none, thanks to Ma-Ma's spell.
It is Gomez who must protect the Addams house, so Fester took his trusty gun and set out on his quest to rescue all the townspeople from the Alien UFO.
--From the NES Fester's Quest instruction manual.