Came to write this. That sentence is clearly nonsense. Either you display the sun, or you don't. Don't display it in the wrong position!
That's a good catch! The clock is inspired by the solar noon (uses sun as the anchor), but shows clock time, so it can be of practical use.
Rereading the post, I notice I haven't made that distinction clear.
Really nice clock.
One nitpick on the day/night line: This is strongly dependent on the latitude, i.e. it kind of collides with your notion of the world clock. Maybe you boldface the label for the city to which it is referring.
Erm, WTF? DST does not change when dawn and sunset occur relative to solar noon. So what exactly is this showing?