In the late 1970's a friend brought me to the computer lab at UWO where I played 'Adventure' (the original text adventure dungeon-crawl) on a mainframe. The terminal I used didn't have a screen, just a dot-matrix spewing output onto fanfold paper: "You are in a maze of twisty passages, all exactly alike."

But come to think of it the earliest computer game I would have played was probably the original coin-op version of Pong and other early-70's arcade games. Followed by the first Atari home systems (which I usually only got to play in department stores. We never had them at home).