Like the page explains: this is not for big webshops with thousands of orders a day and having small margins on each item. You have to see this way of running a webshop in the context of a small business just starting out.
Each payment is checked on your bank account. You can do that once or multiple times a day, whatever your situation requires. Can be easily done with the current banking apps in Europe. The moment you received payment, you can process/fulfill the open orders and mark them as such. Whether that's clicking a button to send a digital file, or packing the order in a box or envelope and sending it.
This might sound like a lot of work, and programmers probably only see the "this and that can be automated"-side of this webshop, but my clients with small webshops happily send their orders across Europe and laugh out loud when they spend only an hour a day on checking payments and shipping orders. They also don't have thousands of orders a day, of course. But they do have the margins to make it worth their while. And if their business grows, they can easily migrate off this webshop.
They are not afraid to put in a little work now, and know they can automate things later.