Your definition for what Proxomitron is is not correct. A server is an application that sits and listen on a certain port number for client requests. Arne's site here is served up by a web server, and your browser is the client.
The same applies to Proxomitron... it sits on a system and waits for a browser to call it into service.
In addition, the other server qualities Proxomitron has is to serve other systems on the network.
Please go check your defitions. Proxomitron is a server.
However Zone Alarm defines it is up to them, but this is how Proxomitron works. If it was not a server, you wouldn't be able to sent requests to it.