huh... I've done a fair amount of home buying and selling, and I've never heard of taking the appliances with you. By plumbing, do you mean toilet? Does the buyer just expect to bring their own toilet from the last house? What a lot of effort.
I'd guess dishwasher and washing machine, appliances which have to be disconnected from and connected back to water inlets and outlets.
I know that, in Germany at least, it's common to take appliances with you when you move. Not sure where in Europe GP is reporting in from precisely.
Yes, this is one of the great German mysteries. Flats are often rented with a completely empty kitchen. The expectation is that you bring not just your own appliances but also your own furniture and take them with you when you move out. This is exactly as inconvenient as it sounds.
Not mention that stuff might not fit their new house, both physically and visually. Its certainly not a common practice where I live in the US.
At one point in the video they are getting an air-conditioner/heat-pump installed...