The personality theory that best justifies the assumption that viewing media causes violent behavior is Albert Bandura's Social Learning Theory (1963).
SLT theorizes that through the process of what Bandura calls "reciprocal determinism", individuals will mimic and repeat the behaviors and dynamics that manifest themselves in their immediate environment. According to Bandura, man and circumstance basically "cause" each other. In other words, we are a product of the society that we create.
The tenets of SLT concede that there is a specific process, both behavioral and cognitive, which facilitates social learning. The process includes the following stages:
Attention depends on the distinctiveness and interest that is paid to something. For instance, a person who has a tendency to prefer violent movies will undoubtedly dedicate a good amount of attention to this kind of media, as the scenario proposes in your question.
Retention is the sustained images and sounds that are selectively stored in our short and long term memories as a result of the attention. Theoretically, someone with a myriad of violent images to remember will be more likely to produce violent behavior, as will be seen in the stage of Reproduction.
Reproduction is the physical and mental repetition of the mental images. It is a human natural tendency, theoretically speaking, that we will "act upon our thoughts".
Finally, Motivation is the final stage of the process of social learning, based on what is at stake. The choice of reproducing behavior is entirely based on what awaits at the end of the choice. In your scenario, pleasure and the presumed mental processes and nervous compensation that occurs during movie-watching or video-gaming may very well serve as motivators to engage in behavior that is perennially in our minds. Other motivators may include peer pressure (negative motivation), financial or popularity incentives, or naturally morbid behavior.