There's no air involved. It's a completely enclosed system. Unless you count the cool/heat of the floors/ceilings affecting the air...
So it's actually a hydronic heating/cooling system? I don't think those systems are typically referred to as heat pumps generally.
I have a gas fired hydronic heating system but I still need AC for cooling(mixture of traditional and mini-split style units due to retrofitting requirements).
I'm also located in a high altitude location but for AC alternatives here we would typically see something like a swamp cooler.
Plus no one has wooden floors. We have cement/epoxy floors. Some neighbors have a wood laminate that's probably mostly epoxy. I don't think you can even get wood floors anymore here. Walls are cement/plaster. Ceilings too.i guess the doors are wood.