The following wiki page on github shows how to use express to handle local requests, maybe that will meet your needs:
https://github.com/appjs/appjs/wiki/Using-express-to-handle-local-http-requests
I have looked but the app.router appears to be undocumented at the moment we should document this from the source code and add it to the wiki. The source code is quite simple if you search for router.js in the node_modules directory, but we should document this functionality.
Simon