In other words, the "commercial video games" used in their research were "brain games" and not Pac-Man, Mario Bros, and Call of Duty, etc.
If you've ever taken a real IQ test where the proxy shows you cards to match or pictures with "missing" data, the 12 video games they used are very similar in spirit. It's not surprising that there is high correlation between the scores of those particular types of video games and real IQ tests.
However, that's not to say there is zero correlation between blockbuster video games like Call of Duty and IQ. Maybe another study will pursue that.