If you want to trace routes as a hint of a path from one place to another, whether by car, bus, or other means of transport, you should not use shapes/polygons, but the Directions service api, which is already available in your script because you are referencing google maps.
With this api you can pass two positions in latidude and longitude or passing the names of the places (in this case specifying in which language the names are) and it will return a list of Latlng points with the suggested path. You can also pass up to eight intermediate points wherever the path passes.
There with this list you draw a Polyline on the maps, it’s easy.
Directions Service
If you want to use the shapes and polygons to draw a drawing over the regions, you will have to recover several border positions and assemble the shapes in the same hand. You have some interesting answers to that
here
If you can extract this map and understand how it works. You could calculate the route normally and then "plot" in this map style. Just a hunch...
– Jhonathan
Post what you’ve already done. It’s javascript?
– Guilherme Nascimento
Yes, javascript. @Guilhermenascimento
– Marcelo de Andrade