Server box

A server box is a computer that exists only to run server software.

Host would be a better term, but it's overloaded in ways that are useful sometimes, confusing at other times.

So there is actually no correct term for this that means only this other than perhaps switch which implies dedicated hardware used in a phone network - which eventually is where all such server box functions will likely be located, that aren't distributed everywhere via a Consumerium protocol.