Another recent study may be of interest: http://www.apa.org/pubs/journals/releases/ppm-1-1-62.pdf

The researchers found that, over three years, those who spent more time playing video games subsequently had more attention problems, even after controlling for earlier attention problems, age, gender, race, and socioeconomic status. Although violent content impacted attention problems and impulsiveness, the total time spent playing games was a more robust predictor. Individuals with attention problems or who were more impulsive spent more time playing video games, even after controlling for initial video game playing.

"These findings provide evidence for bidirectional causality: children with greater impulsiveness and attention problems spend more time playing video games, which in turn increases subsequent attention problems and impulsiveness. This finding does not alter the cause for concern about the potential for video games to contribute to the development of attention problems," the authors write....

As with all nature–nurture questions, the answer
ultimately is that both matter. For the
past 30 years, most of the research on attention
problems has focused on biological and genetic
factors rather than on environmental factors.
This allowed for rapid advances in drug therapies,
but has also caused many researchers and
members of the general public to assume that
impulsivity and attention problems were not
modifiable by experience. This is unfortunate,
as it means we have only focused on part of the
solution. Furthermore, many problems with genetic
bases are clearly enhanced by environmental
triggers. By understanding some of the
environmental influences, we can develop more
effective solutions for children and parents.
More research is clearly needed on the environmental
factors, especially factors that are easily
modified by parents, such as screen time.