The definition of what was classed as a computer game back then is a little hazy to me, but 1947 is the earliest date I have found where a missile simulator game was created by a T.Goldsmith Jr. and Estle Ray Mann. This was followed 5 years later by a graphic tic-tac-toe game by A.S.Douglas, who seemed like more of an academic, focusing on the technological side rather than the 'fun' side of gaming.
In comparison, the next notable computer game was created by William Higginbotham in 1958. This game was called 'Tennis for two' and he has been described as a "fun-loving character and self-confessed pinball player", much more the characteristics of a gamer creating something for his passion.
A few years later was the invention of 'Spacewar', made by three students in 1961. Apparently moving clumps of pixels redefined the word "fun". However, from these simple yet addictive games, a whole new form of entertainment was born into arcades and then households worldwide.
The rest of the 60s introduced gaming into the home with Ralph Baers creating the first 'video' game that could be used on a basic television set which led eventually to the founding of Atari and the release of 'Pong' in 1972, the most commonly known of the earliest games. In the late 70's, we saw the introduction of the eternally infamous classics such as 'Space invaders' by taito, 'Asteroids' and 'Pac-man' with these retro icons bringing a sense a nostalgia to the more "mature" gamer.