Having that poor kid, I'd say, it's better he didn't get that one big gift. Why? Pawn shop it would have gone, as soon as a parent ran short on cash (be it for groceries or booze or medical bills). Plus, those games aren't fun, most of the time, without internet access ($$), subscriptions to the service ($$), a good size TV ($$), and game discs ($$). It's be like buying a quilter the best Pfaff quilting machine they sell - and then telling them they can't have any fabric or thread.
Most of those charities have generic gifts - and that's exactly what they are, generic. Getting something that was at least chosen by someone who knew the age, if not the kid, was probably better than a generic gift from the pool of available things.