Originally created by Taito, this was one of the first Japanese games to commercially make it in the United States back in 1975. It essentially paved the way for Japanese games to work in the American market.
In the game, two cowboys square off in a duel. When the buzzer sounds you move around and attempt to shoot the opponent. Bullets bounce off walls and don't pass through cactus, so shoot accordingly! You also have multiple chances (6) to shoot your target, unlike in real duels.
The controversial aspect of gunfight was the fact that you had to face a human looking sprite. It was the first game to really introduce video game violence, as games beforehand were all about racing or shooting asteroids, etc.
The game also introduced the first early "cinematic elements", where cowboys obviously looked like what they were meant to look like. The background elements (rocks, cactus, etc) also matched the overall feel.
http://www.giantbomb.com/gun-fight/3030-32574/