how's that work? do they operate them on the buyer's behalf?

It's old servers they have already written off and would otherwise decommission. You're basically only paying for power and network traffic.

i'm looking at the site and it seems they don't have this in US

Hetzner doesn't offer dedicated servers in the US. They operate two of their own data centers in Germany and one in Finland. In the US and Singapore they offer only cloud servers, running on hardware in others' datacenters.

thank you