Created for the Nintendo Entertainment System - better known as NES - Nintendo World Championships was designed for a competition, and never went on general sale.
The game features shortened versions of three classics - Super Mario, Tetris and Rad Racer.
Competition entrants were given six minutes to amass points on the games, with whoever came top winning a trophy, a trip to Universal Studios and various other prizes. A detailed history of the contest and its winners can be found on Wikipedia, external.
Each of the 90 semi-finalists was given a grey cartridge like the one now up for auction.
Rarer still are the "golden" cartridges of the same game, sent out as part of a separate competition by Nintendo Power magazine.
Genuine copies of the game are hard to come by, and so the poor condition would not be too much of a deterrent to keen collectors, predicted Chris Scullion, external, games editor for Computer and Video Games.
"It's like finding the rarest Ferrari but with a scratch - you'd still buy it.
"They are considered the holy grail among Nintendo collectors."
In 2011, the same game sold at a charity auction for $11,000 (£6,600) - but it was in better condition.
The auction is set to end on 25 January.