While I don't think violent video games cause violence, it's not a completely ridiculous premise. Interactive video games require you to take and execute the decision yourself, putting yourself in the shoes of the player character.
If you've played the Last of Us 1 or 2, you know what I'm talking about. If you saw it, it would affect you deeply. But actually doing those things hits so much harder. Is it possible that has a deeper effect on us compared to a movie? I don't know, but it's not a ridiculous proposition.