Well let's take a look at violence in the Bible.
The violence in the Bible is righteous violence--meaning it was a clear directive given by God to his glory and justice. Such as the slaughtering of the Promised Land natives.
Violence in the Bible that was not righteous was sinful and condemned. Cain murdering Abel for example.
Then there was the violence that was not righteous or directed by God, yet used by God for the "good of those who love him." You can not use this as an excuse to use violence. You can't say "I hate you so much, brother, because you are Dad's favorite, so I am going to sell you into slavery and God will make you the ruler of Egypt. So you will be blessed by the horrible thing I am going to do to you." No... you can't use God's goodness as justification for sin.
As for video games... Would you invite Jesus to sit down next to you and blow some heads off? I think by you starting this thread in the first place, in your heart you already know. Are you looking for justification to keep playing? Because you will get that here if that is what you want. Or do you want the truth? Personally I hate the truth when it means I have to make some changes in the way I live, but in the end, right is right.
Be blessed.