When was a video game first invented

the 1300s
That's a terrible answer. Let me actually answer your question.
The earliest known interactive electronic game was by Thomas T. Goldsmith Jr. and Estle Ray Mann on a cathode ray tube. The patent was filed on January 25, 1947 and issued on December 14, 1948.[4] The game was a missile simulatorinspired by radar displays from World War II. It used analog circuitry, not digital, to control the CRT beam and position a dot on the screen. Screen overlays were used for targets since graphics could not be drawn at the time.