Most video games are nothing more than puzzles, and puzzles are scientifically proven to be beneficial to your overall cognitive abilities. They help improve memory, problem-solving skills, visual and spatial reasoning, which translates into an overall improvement in IQ.
At the University of Michigan, the psychologist
John Jonides studied what's called "working memory", which is "the ability to maintain information in an active, easily retrieved state, especially under conditions of distraction or interference. Working memory goes beyond mere storage to include processing information." He did this with something called the n-back task which is about learning the right responses when given visual and auditory cues. The subject has to make a determination through the noise of sensory distraction. This is much like those brain games you may have downloaded on your phone before. It also improved the test subjects' abilities to filter out deceptive or 'tempting' choices. A lot of this is applicable to video games.
So aside from the obvious puzzle games, such as the classic Myst series, and even Resident Evil, games such as Call of Duty technically fall within these constraints because they force you to make lightning-quick decisions with the given sensory perception provided: visual cues, spatial awareness, auditory awareness, deception, decision-making.
Your brain is a like a muscle. Games can exercise it.