That seems likely normally not viable in most warm places because the humidity would quickly rot out the floors. Part of the ‘conditioning’ in the name is that quite a lot of water will ideally get removed from the air to control humidity too, and that needs to be drained away

> There's no air involved. It's a completely enclosed system.

So it's actually a hydronic heating/cooling system? I don't think those systems are typically referred to as heat pumps generally.