The study seems to demonstrate "Putting a playstation in a house that didn't have one before causes decreased learning ability relative to not putting in a playstation"
Still room to quibble with that conclusion. The study artificially changed the environment of a house by putting a Playstation in it. The residents of the house would be well aware that they were part of a study, and would attach some importance to the use of the Playstation. They might even allow homework and other academic pursuits to slide in an effort to "do well" in the study of Playstation usage.
This "Observer Awareness" affect is a real problem in studying human behavior. Television rating companies have to deal with the fact that people change their viewing habits when they know they are being studied. Anthropologists have to deal with people acting differently when they know that they are being observed.
Additionally, people treat objects that they get as a gift differently than they treat something they purchase. Perhaps most parents who purchase a Playstation do so well aware of what gaming is and how to incorporate it into their children's lives without affecting their studies, whereas parents who receive a Playstation out of the blue may not know the pitfalls.
So, while this study is not without merit, I would hesitate to say that it establishes anything more than the obvious--that playing video games can distract from academic work. A more thorough study would look into the actual amount of time spent playing video games and the types of games played. It might also look into the affects of video gaming on non-traditional academic skills like hand-eye coordination and general problem solving ability.