The credit card fee is not 12.8% to 15%, that isn’t even a convinence fee. That’s your liquor store not reporting sales and not paying taxes. That’s a big reason why some businesses won’t take cards.
I don't ever assume malice when there is a simpler answer, besides this store is prominent and at the border so they wouldn't be that dumb. The simpler answer is they give a small discount on cash, and a small markup on card purchases to really encourage cash. They are a deregulated liquor state (so they don't have a state ran "Liquor board") which means they can offer much lower prices than just across the border. And I am sure the owner just prefers to go down the street to his or her local branch and say hi to the teller and just deposit cash. Some people just like to do things the old fashioned way. My barber is the exact same way -- he doesn't take card at all, only cash.
But we are well past my economics understanding.
Visa: https://www.visa.ca/en_CAsupport/small-business/interchange....
Mastercard: https://www.mastercard.ca/content/dam/mccom/en-ca/Documents/... (PDF)
AMEX is a bit harder to find, reseller is https://www.helcim.com/ca/american-express/
https://www.smh.com.au/business/banking-and-finance/rba-chan...
Taxation is glorified theft, but in this case I don't care because these are acceptable targets.