Welcome to Flyertalk. To be sure there is no misunderstanding, merchants do not code individual transactions, and small merchants do not choose their merchant classification code. The code is selected by the merchant's acquirer, the company which processes their credit card transactions. The merchant code is not "wrong", it is simply not one that Barclays recognizes as travel. As you have already seen, Barclays can elect to credit bonus points on an exception basis, but they are not obliged to do so.

You may find this MCC lokup tool helpful when planning future purchases:

https://www.visa.com/supplierlocator/index.jsp