Bear in mind also that the routing engine in rwgps depends on the map currently selected (as well as the setting for Walking, Cycling or Driving). One of the OSM layers with cycling appears to give a result closer to what you expected. The "Map" layer is google which appears to favour the cycleway or avoid the hills as grams suggests.
Personal preference, I'd rather go 10km shorter with 200m more climbing. But I've cycled with others who seem to come to a halt on hills and they might choose the other way. Similar for cycle route vs road.