This post comes with an even stronger warning than usual that a single study is just a single study; correlation is not causation; and even well-done studies can't account for every possible confounding factor. In other words, You Have Been Warned.
And yet, this study is pretty interesting!
Typical daily hours viewing television and playing electronic games at age 5 years were reported by mothers of 11,014 children from the UK Millennium Cohort Study....Change in adjustment from age 5 years to 7 years was regressed on screen exposures; adjusting for family characteristics and functioning, and child characteristics.
RESULTS: Watching TV for 3 hours or more at 5 years predicted a 0.13 point increase  in conduct problems by 7 years, compared with watching for under an hour, but playing electronic games was not associated with conduct problems. No associations were found between either type of screen time and emotional symptoms, hyperactivity/inattention, peer relationship problems or prosocial behaviour. There was no evidence of gender differences in the effect of screen time.
This comes via Aaron Carroll, who adds this comment: "Yes, these are young kids, and it’s unlikely that they have been playing much GTA 5 or Battlefield 4. So I’ll look forward to more data. But that this point, it’s hard to point to a large study like this and find a smoking gun. Figuratively or literally."
In other words, if it's a choice between letting your young kids watch more TV or play more video games, go with the video games. Until some other study comes out, anyway.