A while back we discussed video games and movies, and I mentioned that my husband is an avid video game player. Anyway, I know the violence is wrong in games, but what if the characters that you are fighting in a game look more like animals or impossible-looking monsters, then is it still bad? It's not a sin to go hunting.
The difficulty in answering your question is that you are using "violence" loosely. There are parts of the Bible that are violent, such as David slaying Goliath, but this act of violence was not wrong. In this particular case, it was the Israelite's avoidance of violence which was wrong (I Samuel 17). There are other acts of violence that are also mentioned which were wrong, such as the plans to rob people mentioned in Proverbs 1:10-19. It isn't wrong to mention that such evil exists in the world, but it is wrong to participate in such. Being a policeman can be violent, but that violence is necessary to subdue evil (Romans 13:4).
Therefore, it isn't possible to make a blanket statement that violent video games are wrong. It doesn't address the nature of the violence and what is being taught. Is the violence for the purpose of being cruel, for the "fun" of being violent, or to spread evil? Is the violence there to promote standing up against evil and to prevent further harm?