A computer game is a computer-controlled game with or without video technologies involved. In common usage, a "computer game" or a "PC game" refers to a game that is played on a personal computer.
There always must also be some sort of input device, usually in the form of button/joystick combinations (on arcade games), a keyboard & mouse/trackball combination (computer games), or a controller (console games), or a combination of any of the above.
Also, more esoteric devices have been used for input (see also Game controller).
Usually there are rules and goals, but in more open-ended games the player may be free to do whatever they like within the confines of the virtual universe.