To paraphrase the steps involved, because the description doesn't quite make it clear how the casher gets paid without getting caught:
1. Casher sets up as merchant on e-commerce platform like Amazon.
2. Casher takes order from customer.
3. Customer pays with their own credit card.
4. Casher fulfills the customer order by ordering from another merchant (shipper), paying with the stolen card number. The casher creates a brand new account with the shipper just for this purpose. The casher gives the customer's contact information to the shipper.
5. Customer receives order from the shipper.
6. Shipper receives payment from stolen card.
7. Casher receives payment from customer card.
So the casher is paid by the customer, and the shipper is paid with the stolen card. To the shipper, it looks like the customer paid with a fake card. To the customer, it looks like the order was fulfilled as expected.
The shipper gets a chargeback from the card company. If it's not aware of the scam, it's likely to just accept and move on. But if the shipper gets a lot of these chargebacks and knows about the scheme, it can contact the customer (via the mailing address) to ask which e-commerce site the item was ordered from. This may or may not work because some customers will be reluctant to discuss that kind of thing over the phone. So the casher needs to spread the fraud around to lots of shippers and thereby make the investigation not worth the effort.