Video games didn’t start with Pac-Man (1980), Space Invaders (1978), or Pong (1972).

Each of these successful commercial titles repackaged successful elements from earlier games that were designed mostly to demonstrate a visually interesting thing to do with very expensive lab equipment.

Maze War (1973)
This video painstakingly demonstrates the concept of a networked computer, with a split screen showing two different players inhabiting the same game space. None of these three early games featured play against the computer — they were all novel uses of technology that let people play against each other. Maze War is credited with being the first networked game, the first game that uses avatars (in-game representations of the players), and the first game featuring in-game chat.

Spacewar! (1962)
A shooter game, resembling a two-player version of Asteroids (1979) without the asteroids. Players shot at each other in a top-down 2D simulated environment, either floating in free space or orbiting around a central star. The background could display stars from a planetarium program. For more, read this 1972 Rolling Stone article on Spacewar!

Tennis for Two (1958)
Not a computer game, since it did not run on a computer. It was a two-player bat-the-ball game, played on an oscilloscope. No score-keeping, and no way of forcing the players to follow the rules of tennis.

Largely forgotten until unearthed by lawyers searching for a way to avoid paying Magnavox for the rights to Pong. (In 1972, an Atari executive had seen a demonstration of the Magnavox Odyssey, a home game system that included tennis and table tennis games. Later in 1972, Atari released a coin-operated Pong arcade game. Atari had to pay Magnavox a licensing fee, despite Atari’s claims that the existence of Tennis for Two meant that Magnavox didn’t own the exclusive rights to a tennis game.)

See this Brookhaven National Laboratory article on Tennis for Two.