The answer to your question is indeed not obvious from the documentation. In figuring out what the transition function actually refers to, it helps to look into the source code of that function. In the following I walk you through that code and clarify the steps relevant to your question using an example.
So if I understand correctly your output is a route consisting of raster cells?
You could either calculate the length of these raster cells by using the cell size of the raster cells.
Or depending on how your data looks you could try to use r.to.vect and convert your raster cells to lines. Please read the documentation of possible additional steps such as ...