To dream of a video game represents a challenging experience you are having. A win or lose situation. You also may be experiencing a situation where you need to do everything right in order to achieve a goal. The type of video game adds additional symbolism into what kind experience you are having.
Competition that feels casual. Two opposing forces trying to prove they are better than each other. A competition where you are enjoying trying to overcome a challenge faster than someone else.
Negatively, a video-game may reflect a competition between people who want to get back at each other. Two people trying to humiliate each other that they are better than the other person. Petty feuding or teenage competition. A cold or casual view of a competition with big stakes.
Alternatively, a video game symbolizes an escape from your problems, instead of confronting them. Intentionally wasting time.
Example: A man dreamed of seeing himself stealing 2 video-games from someone who didn’t like him. In waking life he was running a business and confronting a dishonest person who was trying to compete with him illegally. This dishonest person who was trying to compete with him illegally had a very casual attitude about competing even though there was a lot of money at stake. The dreamer has to strategically take legal actions to defeat the illegal competitor, but the competitor just kept trying to compete anyway.