If your reference is to the below tutorial, then I would guess the kitchen display most likely list of delivery orders.

https://www.odoo.com/slides/slide/business-flow-restaurant-1112?fullscreen=1

The reason for this, Odoo launched the kitchen display App and self ordering functionalities with V17 release. The tutorial is prior to V17

My best estimate would be that their kitchen display is a filtered (by contact and grouped by stage or scheduled date), kanban view of the delivery orders. Something like this

If you need to achieve this, you would need to enable the 'extra step during checkout' option from settings > website > Shop-checkout process section

Configure the extra step form to add the 2 fields 'Delivery date' and Delivery address. (Have only the values that of the restaurant outlets visible)

This is an extremely high level concept and not a comprehensive step by step solution. Moreover with V17, self ordering might provide better possibilities. It has eat in / take out option along with service and payment.