This is the game of Spacewar!, created by Steve Russell and others in the early 1960s.
The game features two spaceships, called "the needle" and "the wedge", engaged in a dogfight while maneuvering in the gravity well of a star. Both ships are controlled by human players. Each ship can fire its rocket engine to maneuver, and can shoot torpedos with a limited lifetime. Ships remain in motion even when the player is not accelerating. Flying near the star to provide a gravity assist is a common tactic. Ships are destroyed when they collide with a torpedo, the star, or each other. If a ship or torpedo moves off one side of the screen it reappears on the opposite side.
To play the game you will need two gamepads connected to your computer. The game uses only the four action buttons on the right of each gamepad.
The left button turns the ship counterclockwise, the right button clockwise. The lower button causes the ship to fire its rocket engine, accelerating it forward. The upper button causes the ship to fire a photon torpedo.