Remember, unlike that map, the Earth is curved. So when it's put into a 2D format from a 3D reality, it will come out curved. That route is a shorter distance than what a straight line on the map would appear like. The Earth is not a sphere, but more of a squashed oval. Going on a more southerly route means more distance needs to be covered.

Now, generally airlines have logistics departments that work the routing. There are many factors which determine how a flight routes, and it is rarely straight. Even with GPS and the technological ability to fly direct point to point, most planes are still routed from beacon to beacon or nav point. Factors that influence this are airspace rules (restricted spaces around military zones, or countries that don't want foreign planes in their airspace like North Korea), safety factors like distance to diversion airports or radio dead zones, weather..either avoiding the bad stuff or taking advantage of the good weather.., and fuel savings. For example, avoiding a jet stream headwind for 12 hours by going north or south of it, or above it.