I don't really get the linear comments here. Sure, the map is a rectangle, but there are towns an cities all over. There is no clear path from bottom to top. In all likelihood like you leave the early areas by train, and who knows where you go after that. If you get to that first big city, there is an entire area back south that is untouched, and it is unclear where else you would go next. There is an exit to the big area to the south, which also would connect to a path back north that looks like it goes to the next big city. There is a path to the east, which leads right into a cliff, and it is totally unclear where that goes. And there is a railroad to the east, that looks like it goes into a tunnel and goes to the town to the east before continuing on to who knows where. And there is also a path to the west that heads off into a mountain without an obvious exit.
If we look at the next big city, it may have path exits in all four cardinal directions, two of which potentially split into two paths (I'm unsure if that dragon head in the south is an entrance or not). Both the east and west paths go to multiple locations, but are ultimately dead ends. Which comes first is totally unclear.
And of course, so much of the linear talk is base on assuming that the map is a perfectly accurate representation of the region. While this seems safe to assume, as it pretty much was for Alola, I think we have reason to believe that is not the case here. I noticed something in Codraroll's post on the last page when comparing the image of the first town to the map. While Codraroll was pointing out how small the town was and how isolated it was, I was noticing that it had 5 buildings. The map only shows 4. This might seem a minor detail, but if it means that the map is more of an artistic interpretation of the region, and not supposed to be taken as a 1 to 1 representation, it means there may be a lot more to Galar than people are assuming. EDIT: This is further supported by the image of that next town showing at least 6 buildings (including a Pokemon Center) in addition to the stadium, when the map only shows the stadium and 3 other buildings total.