On the surface of a sphere, the shortest distance between two points is along a great circle route (which is the equivalent of a line in spherical geometry). Polar map projections preserve straight lines as great circle routes, but, e.g., Mercator projections do not.
If you're looking at a 5 km × 5 km topo map, the difference isn't particularly significant. If you're looking at a map of Europe or the United States, it is (note that many airline routes seem to follow curved lines--it's because the shortest distance is that curved line).
For regional maps it doesn't particularly matter, the map will be in a projection that has relatively minimal error, but a straight line in most projected coordinate systems will not be the shortest path between those points.
It doesn't mean that there is a viable route on that line or that that line is the preferred one.
That one is really bad, imo