I know what has happened isn't ideal, but it's pretty clear that they're trying to sort it. From what you've said it doesn't sound like they have tried to fob you off, but have told you the truth.
The comment that I quoted above....I really hope you didn't say it
The guy at the other end of the phone is more than likely a minimum wage worker trying to pay the bills like all of us. He's most likely bending over backwards to get that 20 quid for you.
As a guy who's been in that position, let me assure you that these people
really do want to make sure you get your stuff, and it's comments like that that makes people not want to do anything other than the bare basics to get things sorted out. He doesn't care about GAME as a company any more than you do - he cares about eating, having a roof over his head, and probably trying to enjoy the small pleasures he has at a weekend with the little cash he has left over.
If a customer had said to me that they'd probably not spend the free 20 quid I'd managed to wangle for them, I'd politely thank for their honesty and revoke the offer.