It's not quite clear from the video but it looks to me like you park up in the garage, and there's a garage door on the other side. So as you 'check in', I guess the 'human' side you drove in on, that door closes, and then the other side opens for the robots to collect the car which I'm guessing is also where the car storage is.

Sort of feels like those videos you see of high tech warehouses where the human workers really only operate on the outskirts of the building, and everything central is completely automated (picking, sorting, storing, inventory etc)