The arcing line is nothing more than a stylistic riff to show that you are "hopping" from point to point. This style predates pre-dates consumers having ready access to flight, e.g. It would be seen in pre-war films in those interstitial "cards", illustrating that the story was moving on. The hop is always upward, to indicate "up" or "passing over" (that part of the story).
The thing today, where every travel map shows a fastidious capture of actual surface routing (for consumers for whom it makes no difference), is a modern craze owing to map apps and nav's.
In this case, the stylistic riff is being used to say, flat-out, this isn't your actual surface route. If they had drawn a plain straight line, it could be mistaken for that.
The most direct route is always a straight line, even in the Southern Hemisphere. There's no such thing as a "Great Circle route" that is faster by flying a curve. Remember, we are deliberately looking at flat projections of the surface of a sphere. We are aiming to ignore the one curve you must follow, the solely vertical curve of following the surface of a sphere.
At this point we must discuss the Mercator Projection, a particularly defective kind of map where longitude and latitude lines are forced to be square. You can spot it instantly, when state and province borders are mis-shown intersecting square without bends: Ask any mapmaker, that isn't how things are! This fault also makes Greenland appear bigger than Australia. Above, Facebook and Rome2Rio get it wrong, using this shabby projection. Rome2Rio shows the actual surface route, but since they have bent the map to make curved lines square, the route bent with it.
They call this mistake the "Great Circle Route". Mmmmkay.