transport.php & gosmore.php are called from yours.js. This javascript file has all the client side functionality required for a routing application. Yournavigation.js contains the website specific javascript functions (initialize the map, connect the UI to the yours.js functions.
transport.php is needed to make cross-site calls to nominatim (it is a proxy). So if you click on the map or type a streetname then the call to nominatim for the geolookup is routed through transport.php.
gosmore is indeed called to give the routing result.
The main functionality is all contained in a javascript class called “yours”. This class manages the list of route sections (the route between two markers). When a section is complete (i.e. 2 markers have been placed or one marker is moved) then the class member function “draw” is called. This function calls gosmore.php to give the route. The route result is then parsed by “parseKML” (or in a future version “parseJSON”) which will load the route in OpenLayers.
PS. please post new questions about YOURS in this thread. No need to create a new thread for every question. Thanks!