Who invented video games

Technically, there is no one single inventor of video games.

However, the earliest known interactive electronic game was created by Thomas T. Goldsmith, Jr. and Estle Ray Mann on a cathode ray tube in 1947. The game was a missile simulator inspired 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. So, according to this, Goldsmith could be credited with the first video game.

The following answer could also be considered correct:
According to Wikipedia, Ralph H. Baer "is noted for his many contributions to games and the video game industry. In 2006, he was awarded the National Medal of Technology for inventing the home console for video games and spawning the video game industry. This guy happened to create and develop what was known as the Magnavox Odyssey in 1972. Baer is credited with developing the first video game on a console, and the first console to use a light gun; similar to the gun used in Nintendo's duck hunt."

The very first idea for an interactive electronic game came in 1951 when Ralph Baer, instructed to build the best TV in the world, had the idea of including a game into the TV. However his superiors didn't like the idea, and so it took another 7 years before the idea would emerge again. In 1958, physicist Willy Higinbotham invented the first Pong-like game on an oscilloscope, to stop visitors to his lab getting bored. However it was in 1961 that most people agree the first true computer game was invented. Steve Russell, a student at MIT, used a Digital PDP-1 to create Spacewar. Though the graphics were extremely primitive, Spacewar inspired Nolan Bushnell to create a version of Spacewar that could be played on a home TV. Creating 'Computer Space,' the first home video game was born.