Edit - Lotta video game apologists in this thread. Look past your capitalist dependency on causing violence to other people/animals, and recognize what you're doing. Stop Video Games.
Video Games are a media (superstructure) that reflect the economic base we live in. It is part of the cultural hegemony we live under, that the state uses to justify itself and capitalism.
Violence is an inherent part of this ideological propaganda apparatus (along with patriarchy, racism, sexism, transphobia, homophobia, anti-communism, capitalist normalization etc.)
All media influences the people that receive it. It is "pure liberalism" to believe it does not. If you're a Marxist, you must stand against video games under capitalism.
The actual truth is more insidious: just like action movies and any sort of action literature, violent video games primarily hinge on the idea of legitimate violence doers doing violence - the chosen heroes, the formally sanctioned enforcers of the system, monarchists, and other narratively accepted legitimate violence doers.
They're just another facet of media that's reinforcing the idea that it's ok when the people whose job is doing violence do violence to someone. They can only "cause" violence from the consumer when they inspire that consumer to join up with one of those formally legitimized violence-doer groups like the police, military, etc. The same was true for movies before that, like how the secret service agent who saved Reagan was inspired to join the secret service after watching a movie (starring Reagan, ironically) about them. Though of course saving Reagan is a degree of heinous behavior well above most cases.