My 16 year old has the game. Its a 16 rated game here in SA, maybe its a different version I am not sure. But last year when he got it, we had a major ding dong and the whole x-box console was taken away from him for 3 months. The game is addictive! He is one of those kids who do get quite addicted to games, wow was another one, but there is just something about this game - he would rush home to get playing it, he didn't even socialize with his friends at one point when he first got it. He failed some of his mock exams and i took the console away. Yes there were some melt downs and tears and a bit of shouting and screaming. He tried every avenue to get it back, started out with some tantrum type behaviour which didn't work as I extend the ban because of that, then there was the not talking to me, then there was the nicey nicey tactic, i have never had so many cups of tea made for me ever as during that time
. After a few weeks he accepted the idea, and started reading his books that were half read... and he did his schoolwork which he fell behind in.
Now he only plays on weekends, its still banned in the week...
I am the parent and although he is practically an adult he was hardly behaving like one.
I really do not think that he is going to miss out socially by not having the game OP. It wont end here, once he is done with that game, it will be something else. I think its not really about the game as such, i think is a power struggle. 12 years olds are at the inbetween age, not so much a child but not yet an adult, so trying to find themselves really..... Stick to your guns. Think of the lesson learned in the long run. If we give in to every little demand they make, where is it going to end? Every child in the school does not have the game, I assure you. I know he wants you to think that, but there are a lot more parents like you, than you think 
You sound like a good mum OP. 12 year olds are hard work. I have had two of them 