There's a good book with a catchy title that talks in depth about this very thing.

There are a few summary points:

• In general terms: Video Games > Pleasure Reading (Non-Educational) > TV
• The TYPE of video game, TV, or reading you do matters much more than the format, for example:
• Puzzle solving games like the Zelda series is much better for the mind than Call of Duty type shooting games.
• Novels, especially of a high complexity, are better than Magazines.
• Shows that require you to think (examples used were Sopranos and The West Wing) are better than those that don't (examples used were Big Brother and American Idol).
• Video Games as a non-educational activity improve test scores the best because they are interactive, you have to both analyze a situation and then respond to it. This is especially beneficial if you are solving puzzles.
• Pleasure Reading, while not interactive, requires you to take in and analyze situations in order to understand the story. The more complex the analysis required, the better.
• Watching TV only requires sporadic analysis. In the more complex show your brain seeks to solve and connect storylines to make sense of it. In the less complex show you only passively absorb.

In the book they looked at a study which took groups of kids/teens of varying ages (I remember it being 4th grade, 7th grade, and 10th grade) and divided the kids into 4 groups: Gamers, Readers, Watchers, and Listeners. The Listeners did nothing but listen to popular music and socialize. They tested all the kids at the beginning, middle, and end of the experiment. They used the test average from previous years as their baseline for comparison.

They found that kids that played puzzle-solving video games improved their scores the most, readers the second most, and watchers the third most. Listeners scores actually decreased as compared to the average.

The book also looks at a second study that used adults and finds similar results. Gamers > Readers > Watchers > Listeners.

The tl;dr of it is, doing something with your brain is good regardless of the format, and the more interactive and engaging that medium is the better it will improve your thinking.

/u/Rambo_Brit3's and his/her wife need to be more concerned with WHAT video games their son is playing rather than the fact that he enjoys video games. I don't know how complex "League" is (I'm assuming League of Legends simply because of its popularity). And the complexity of the game is an important factor.

At least he's not getting stoned and listening to pop music.