In the WebSocket spec, it only exists to open a connection to a url on a port, there is nothing about listening to a port for connections. You could open a connection to a server which can relay other websockets data, but you can't open a connection to another client. There is nothing in the spec to create a server basically.
That doesn't make any sense. The browser server just responds to websocket requests the same way a server would. The other browsers acting as clients wouldn't even need to know it was a browser just that it was acting as a websocket server.
The same way that websocket servers currently listen for connections. There are websocket servers in production and they have a standard way to listen for connections. All you would have to do is implement that same functionality.