1972, the year Pong and the Magnavox Odyssey came out.
Actually Invented in...
1948, when Thomas Goldsmith Jr., a professor of physics at Furman University, patented his horrendously badly named idea, the Cathode Ray Tube Amusement Device.
The Amusement Device was based off old military radar displays, which were just dots on a screen. They figured you could put some kind of overlay on the screen with pictures of aliens on it or whatever, and you'd have a rudimentary game where you could shoot projectiles at the bad guys. Despite being only kinda crappy, it was still too expensive to be marketable and only a few prototypes were ever built.
The second video game came out three years later. British electronics company Ferranti built the NIMROD, a computer designed to play one game and one game only, the classic game of NIM.
Go on, play NIM online so you can relive the forgotten golden age of video games: I'll wait.
Back? Yeah, that sucked; especially because the bastard computer keeps winning (obviously, it cheats!). Like all computers from those days, it was the size of Adam West's Bat-computer, and simulated a game that's played with 16 match sticks. So the first computer game was only useful if you were the world's greatest NIM player, or just extremely short on matchsticks.