Debit cards provide immediate verification of the customers ability to pay and in many cases provide immediate movement of funds to the merchant. They know they will get the money, and they get it fast.
That is exactly what happens when you pay with a paper check at Walmart. If you don’t have enough money in that account the check will not be approved. If the check is approved, that money comes out of your account immediately.
Those are probably check verify transactions. They use the same network that debit cards use. I’m sure Walmart pays for that. I’d still rather type in a PIN than carry a check book and write a novel at the checkout. Or maybe you don’t have to make out the check since it’s superfluous at that point. I assume you have to show ID too.