That's a very normal Seiko (or similar) receipt printer. I spent a lot of time programming them. Humorously, the programming manual is marked "confidential" (I guess to make it hard for anyone to make compatible printers), but there are copies of it all over the web, and there are plenty of compatible printers ;).

The POS app that I worked on (not related to the one shown in the video) also went to pretty serious lengths to get rid of the pause between the user pressing "enter" and the receipt coming out. The store operators rightfully insisted on this, because they wanted to keep the checkout lines moving as fast as possible.

I liked those printers and remember wanting one for myself even though I had no use for it. They start at around $200 and take up space, so I managed to resist.