I was looking into how the days get longer and shorter (I live at a higher latitude) and I stumbled upon this picture showing how day and night look like on a flat earth. To me, it doesn't make sense how the December solstice works, seeing how the sun manages to selectively avoid regions, yet stretches along Antarctica. If it was a spotlight it would be circular, no?

Looking at the cities in question for Christchurch and Bloemfontein, they both appear to have sunsets/sunrises at the same time (using data from timeanddate.com).

Can someone explain this phenomenon on a flat earth to me?