Um, there actually is a fair amount of evidence that violent video games influence people's thinking.

Just as a quick gut-check, ask yourself this: if they didn't change your thinking, why would you play them? Assuming they don't offer any level of excitement or entertainment, what is the point?

Evidence: the US army uses FPS to train people for combat, and there is a longer history of what it takes to train people to shoot people: switching from round targets to human-shaped targets makes it a lot easier for soldiers to aim the gun at a person before pulling the trigger.

Now clearly most people who play violent video games don't turn into mass killers, but to say that the deep immersion of a FPS doesn't change your thinking is farcical on the face of it.