Once you have inserted your coin(s) into the cabinet of Bally Midway's 1989 basketball arcade game of Arch Rivals the game shall display the text "TODAY'S GAME:" with the name of a randomly-generated team, the text "VS." and the name of another randomly-generated team below it; if you do not like the teams the game has chosen, you can press the Punch Button until you are happy with them, then press either Start Button to start up the game. The text "CHOOSE THE PLAYER YOU WANT TO CONTROL" will then appear upon both sides of the screen - and as you push the joystick up, down, left, and right to do it, the Coach's Notes for each player will be displayed at the bottom of the screen. Once you have pressed the Pass Buttons, to confirm your choices, the text "GET READY, (PLAYER NAME)!" will appear on both sides of the screen, with a shot of your chosen players in their changing rooms below it; the screen will now cut to a shot of the court with your two chosen players stood in the centre of it as the referee throws the ball into the air and the first quarter begins. A full game is comprised of four quarters, each one four minutes long - and each team has two players, but the objective of the game is to outscore your opponent until the final buzzer sounds. A player can call for his CPU-controlled teammate to pass him the ball or to shoot it, and if the score is tied after four quarters, a sudden death overtime period (which is one minute long) will get added, in which case the next basket to go in will win the game for the team who scored it; if neither team fails to score in the overtime period the game will end.
The difference between this game and all other basketball titles is an ability to freely punch an opposing player without penalty and steal the ball away, given that the referee will only call a foul for a shot clock violation. Also unique to the game are various on-court hazards such as soda cans and candy wrappers thrown onto the floor - and if a ballhandler steps on these he falls onto the floor, allowing his opponent to steal the ball from him. Players can also fall over the referee, in the same way as the objects on the floor, as well as steal the ball with a maneuver called the "flying leap" where the player will jump forwards at the opposing ball carrier; if the maneuver misses, the player will roll along the floor, but if it is successful, the player will tackle the opponent holding the ball. In the arcade version, performing the "flying leap" will cause your player to pull the opposing player's shorts down, revealing his underwear - but, on home ports of the game, this was left out. Whenever a basket is scored (for either two or three points), there are many random cutscenes that may be triggered; one scene has the coach shouting at his team's players, another features players from the team who the basket was scored against groaning in disgust, and two scenes have cheerleaders shouting "Go, team, go!" from the HC-55516. The basket backboards can also occasionally be shattered with a rim-rattling slam dunk - and this effect was later reused in NBA Jam. The TV studio in the game is that of the fictional WIDB-TV; it is shown after the end of each quarter, and also at halftime. In addition, after the first and third quarters, a "Coaches' Corner" screen also appears, providing tips on how to become a better player - and a cheerleading squad performs the halftime show. The final statistics are shown at the end of the game, showing how many points the player (or players) scored, along with the numbers of steals and rebounds, and shooting percentages.