Video games have been shown to raise aggression when played and directly afterwards and much of the evidence I have seen points to the effect described above whereby violent people are attracted to violent video games.
There is little to link violence to explicit video games but some that suggests in some cases it may increase anti-social behaviour.
EDIT: As downgraded wil procide sources and more info:
Firstly a caveat - research on violence and video games is limited:
From Adachi et al (2011) The effect of violent video games on aggression: Is it more than just the violence?
"Experimental research has shown that playing violent video games produces higher levels of aggressive cognition, aggressive affect, physiological arousal, and aggressive behavior (in the short-term) than nonviolent video games. However, there are two major limitations with these investigations. First, the majority of experimental studies that have compared the effects of violent versus non-violent video games on aggression have failed to equate these games in terms of competitiveness, difficulty, and pace of action. Thus, although the common finding is that violent video games produce higher levels of aggression than non-violent video games, other unmatched factors beyond the actual violent content may be responsible for the elevated levels of aggression. Second, previous experimental studies have tended to use a measure of aggression that may also measure competitiveness, leading to questions about whether violent video games are related to aggression or competitiveness."
On the subject of violent video games having negative outcomes:
Gentile and Anderson in taking sides (pp1098-5409)
"Gentile and Anderson believe the research has made it clear that playing violent videogames leads to violent behavior. These researchers claim that several things happen when a child is playing violent games: an increase in physiological arousal, aggressive cognitions and emotions, aggressive behaviors, and decreased pro-social behaviors."
However the co-author (the book is a debate type thing) states:
"that there is not a causal connection between violent video games and violent behavior. In the second article, she summarizes several of her relevant research studies, including multiple qualitative and quantitative projects, a survey of over 1,000 middle school-aged children, and in-depth conversations with 42 youths in focus groups. While she allows that some individuals may have bad experiences with video games, she reports that playing such games, even violent ones, is a normal part of adolescent development. Indeed, they may even have pro-social and relationship-building consequences"
Williams (2011) The effects of homophily, identification, and violent video games on players.:
"After an experiment with 148 male participants, results indicated that skinning a video game character to physically resemble the player led to greater identification and psychological involvement with the game's character but did little to impact the feeling of presence. Exposure to violent content also led to greater physical hostility than exposure to nonviolent content. An interaction effect revealed playing a violent game with a character physically resembling the player led to even greater hostility."
Sester and Bartholemew (2011) Violent and nonviolent video games produce opposing effects on aggressive and prosocial outcomes.
"Experimental studies routinely show that participants who play a violent game are more aggressive immediately following game play than participants who play a nonviolent game. The underlying assumption is that nonviolent games have no effect on aggression, whereas violent games increase it. The current studies demonstrate that, although violent game exposure increases aggression, nonviolent video game exposure decreases aggressive thoughts and feelings (Exp 1) and aggressive behavior (Exp 2). When participants assessed after a delay were compared to those measured immediately following game play, violent game players showed decreased aggressive thoughts, feelings and behavior, whereas nonviolent game players showed increases in these outcomes. Experiment 3 extended these findings by showing that exposure to nonviolent puzzle-solving games with no expressly prosocial content increases prosocial thoughts, relative to both violent game exposure and, on some measures, a no-game control condition."
Bosche (2010) Violent video games prime both aggressive and positive cognitions.
"Previous studies have shown that violent video games prime aggressive thoughts and concepts. Interestingly, positively valenced test stimuli are rarely used in this field, though they might provide useful information on the nature of the emotional response to virtual violence and its associative structure. According to the General Aggression Model (GAM) and its extensions (Carnagey, Anderson, & Bushman, 2007), normal negative reactions to violence are expected. Alternatively, playing violent video games might be construed as engaging in positively valenced playful fighting behavior. To test the potential of violent video games to prime positive concepts, N = 29 adult males played either a violent or a nonviolent video game for 20 minutes and were subsequently tested in a standard lexical decision task consisting of positive, aggressive, nonaggressive negative, and neutral target words. The data show that the violent video game primed aggressive concepts as expected, but also raised positive concepts, and did so independently of the participants’ history of playing violent video games. Therefore, the results challenge the idea that violent video games inherently stimulate negative concepts only."