Atari kicked off the arcade frenzy of the 20th century with Pong, in 1972. Shortly after, they made Space Race, a two-player game where the goal was to reach the top of the screen before the other player while avoiding obstacles.
Noticing the phallic symbolism of the traditional joystick, Atari thought they'd play a joke and make the controls a little different with their next game, Gotcha.
Those are breasts.
The public didn't take it very well, and the game was not successful. Later versions of the cabinet had the modified "joy"sticks removed.
As for the game itself, it was the very first maze game in the arcades. One player chases the other around a maze as the walls slowly shift around. Here's a gif of the game in action.
Maze game, or groping simulator?
I wonder what Jack Thompson would say.