I think as a start, I would use a vector drawing prog like Inkscape or Illustrator to get the linework done. All those straight lines just beg for it I think. If you are asking about the style, I think the subdued colours are what gives it the feel that it does. I would just pick the colours directly from this map and use them as your pallet. For the woodcut water markings, I would just see if the vector prog could select the land and stroke larger grown selections of it using thinner lines as you go out. .