Your average college student who took a semester of stat learned that correlation does not imply causation. However, it still can reflect causation; in the real world of science, early-stage association studies find a correlation, from which further experiments can be designed to assess a causative link. If further, more refined experimentation confirms this trend, and a satisfying mechanism is given, consistent with other knowledge on the subject, then we do consider it a causative link.

Nobody has actually proved that smoking causes cancer, but experiments with cell cultures on petri dishes exposed to smoke, experiments on animals, and what is known about the chemistry of smoke, the biochemistry of cells, supports very strong evidence for a causative link.

There is extensive evidence, from before the time of video games, to show that children who are exposed to violent imagery tend to become more violent themselves. There are, indeed, cases where individuals who went on murder rampages openly acknowledged that they were influenced by video games. During the Vietnam War, the US army showed violent films to new recruits to desensitize them to violence. The trend continues today, in which the US army offers free downloads of war games.

The real issue here is the odds ratio: given a logistic regression in which we measure a binary outcome of serial killer vs. non-serial killer, will playing more hours of video games increase the odds ratio of a serial-killer-positive outcome? Is there an interaction between age and hours of video games played per day? How violent was the video game? Both common sense and extensive psychological evidence suggest that young kids who are exposed to violent imagery all day are at increased risk of violent behavior.