That game would be Donkey Kong, perhaps the best known of the so-called retro games of the early 1980s that were the first seeds of the video game industry, which has grown into the entertainment behemoth of the modern age.
In fact, despite so much hyperbolic talk about the skills necessary to master Donkey Kong that you wonder why winners aren't eligible for a Nobel Prize, surprisingly little of the documentary concerns itself with actually how the game is played.
Rather, filmmaker Gordon, who edited and produced the excellent "New York Doll," focuses on the psychological dynamics of rivalry, concerning himself with what it takes to get to the top of anything, even video gaming, and the lengths people will go to stay there.
The rivals here are such classic American types that no fiction writer could have improved on their characters or their differences from each other.
On one side is Billy Mitchell, who set an iconic record of 874,300 points for Donkey Kong back in 1982, when he was a teenager featured in a Life magazine photo spread on the nascent gaming phenomenon.
In the years since, Mitchell, now a hot sauce entrepreneur who lives in Hollywood, Fla., has stayed close to Twin Galaxies, run by the unconventional Walter Day as video gaming's governing body. Vain, hyperconfident, given to wearing American flag neckties and saying things like "if you want your name written into history, you have to pay the ultimate price," Mitchell is not averse to being viewed as the Darth Vader of Donkey Kong.
On the other side of the continent in Redmond, Wash. -- and on the other side of the psychological divide -- is doofy Steve Wiebe, the kind of never-No. 1 nice guy family man who can't even get people to pronounce his name correctly.
Looking for some control in his life after he was laid off by Boeing, Wiebe, just as obsessive as Mitchell but in a kinder, gentler fashion, turned his analytical mind and hand-eye skills to Donkey Kong a decade ago. And to the astonishment of the gaming world, he became the first player to best Mitchell's record. At which point, all hell broke loose.
For the really compelling part of "King of Kong" is the machinations, shenanigans, conspiracies and contretemps that take place after Wiebe submits the tape that makes his claim for the top gamer spot.
Twists, reverses and surprises are continual, extending not only to the film's last frame but also, according to a recent New York Times article, even beyond it.
Director Gordon, who served as his own editor and cinematographer, has made the most of the superb access he had to the rivals and eccentrics of the Donkey Kong world. While "King of Kong" sometimes feels too Manichean, too concerned with painting its rivals as ultimate good and evil, it more than lives up to the opening William S. Burroughs quote, which posits that, more than anything, ours is a civilization based on war and games.
MPAA rating: PG-13 for a brief sexual reference. Running time: 1 hour, 22 minutes. Nuart Theater, 11272 Santa Monica Blvd., West Los Angeles, (310) 281-8223.