For those who don’t know how it works, a business has to have a “merchant account” to be able to accept and process credit cards. (And debit cards, although in theory those can be handled separately.) There is nothing about having a business banking account that automatically allows the business to accept cards… they have to have a specific account with a provider of “merchant services,” as the service is called.
You can go through your commercial bank, and if you’re big enough, that can be a good option. Most merchants will go with providers that have lower rates and better terms for small or specialty merchants - the convenience store that does 5,000 $10 transactions and the jewelry store that does 50 $5,000 transactions in a month would probably not use the same provider.
The smaller the average transaction, the higher the volume, and the higher the rate of fraud and misuse, the higher the merchant charges go. Target might pay 5 cents a transaction and 1 percent as its service fee; a convenience store might pay 35 cents and 2.5 percent, or more.
In general, when you find a business that won’t take credit or is oddly selective about it, it’s because they don’t want to pay the service rates for their category or operation. Sometimes it’s because they’re cheap bastards and would rather inconvenience some large part of their market rather than take the tiny hit on credit purchases. Often, though, their service rates are high enough that it’s a significant factor for hundreds or thousands of low-dollar transactions, and they just can’t afford to take the discount.
I’d bet the amusement part has had its share of fraud issues, possibly not all on the customer side, and can’t get general credit card services except at proportional rates - $1 and 5%, or worse.
Also, most merchant services accept all cards, or most of them. When a merchant only accepts one card, like Discover, it means they went right to that card’s sales division and worked out a deal, rather than going through the more common combined ‘brokers.’
Also also, it is illegal in most places for stores to either charge a surcharge on credit purchases, or a “cash discount.” Consumer protection laws, for good or bad, require sellers to treat all forms of payment as equal. So the cost of the credit transaction has to be factored into the price, and if it’s high, that screws and discourages cash customers.