Some computers are unable to play BO ll.. depending on their graphics. So maybe a low graphic game will be able to work for you but a high graphic would not. It doesn't have nothing to do with the space the computer provides, it's just what type of year and if it is a good re-solution. Old computers are up to date remember that they will not contain the same as a new computer or latop that comes out.
Best solution to do is message them see if they can give you a reason towards why you are not allowed to start the game. Maybe their answer will be better then mines.
I suggest just buying a PS3 or Xbox360 or one of the new systems which I think for now they only have ghost in the new systems. Since computers seem to have more problems then systems do, easier to get banned..
This is your decision remember! Good luck hopefully my response will help you out.