It doesn’t have any concept of registered users since it treats a visitor as a customer who may or may not have visited the site before. It is not required to be a user of the site to purchase something using this plugin.
A visitor lands on the product page, then he can purchase an item using a quick checkout. Nothing else is needed. The order will be saved in the “Orders” menu of the plugin so the site admin can see what was purchased and by who.
Since this plugin is free, you can set it up on a test site using the following tutorials:
https://wp-express-checkout.com/wp-express-checkout-plugin-documentation/
Then you will get a good idea of how it works.