Does it help to point out that the water path looks suspiciously like the day/night line on a map?

Like this: https://svs.gsfc.nasa.gov/5477/

yes!! why is that ? :)

The day/light line is a great circle. The "straight line paths" are great-circle segments.

It's going South and then trying to close the loop from behind. It gets interrupted by land before the loop closes.

Hope it makes sense.

Open the linked paper and scroll down, they have images of the path on a globe as well as the flat map view.