Video games are symbolic of total and utter escapism and mindless thought. They are a modern phenomenon that will have very different symbolic meaning based on your personal relationship to them.
The diehard gamer will have a joyous experience of that escapism, while a critic might hold a more judgmental perspective. Where you stand on this continuum will provide the full picture for your interpretation. There is a perspective of video games that connects to a type of skill building; however, those skills have very little practical value outside of the realm of playing the game repeatedly. This is where the element of mindless thought enters into the symbolic meaning of video games.
The presence of a video game in a dream is an ironic appearance of detachment and should be considered as a possible defense against whatever the unconscious mind may be attempting to express.
If someone in your dream is playing a video game, understanding the character aspect in you that the person represents will identify what area of your consciousness is avoiding reality.
[1]