You should claim against
FGW▸ for the ticket you subsequently bought. It is that ticket (if still in your possession - but not a deal breaker if it has since been retained by a barrier etc) they should be refunding. They were the retailer and it is they you entered into a contractual arrangement with. Internal systems should be able to be checked to confirm the original ticket was not collected and/or the machine you attempted to use had a fault at the time in question.
They should not be charging you and Admin fee for something that was beyond your control.
Make the claim in writing, submit the ticket you subsequently bought (keep a copy), if you don't want the refund in Rail Travel Vouchers - say so. Let us know how you get on.
In the meantime, welcome to the forum, philips999.