You can print the player movement. On the Preferences tab, select the Behavior category, then check the box next to "Show the Print button on Player Movement dialogs."
Setting up the ability to print receipts with seating assignments on buy-in/rebuy/add-on is certainly possible (as evidenced in the video), but does take some work. I believe the person in that video used the Find feature on the various buy-in/rebuy/add-on dialogs, along with a player ID added to the database. The ID was then used by another application to print ID cards with barcodes. So a scan of the ID card matched an ID of a player in the TD's player database. The Find feature had the "Auto perform action" option enabled (a checkbox on the buy-in/rebuy/add-on dialogs), so when scanning an ID card, the ID matched a single player, which caused the TD to automatically perform the action (buy-in, rebuy, or add-on) and printed a receipt with their seating assignment.