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.
But seriously yeah video games cause violence but not in the way most think.
For example, how many kids have signed up for the US or a NATO aligned military after playing call of duty or battlefield? And have gone on to participate in violent acts as part of those armies? Or become a cop?