The earth is rotating too and it’s tilted so depending on the latitude you won’t have a simple elliptic path when you expose over days or even weeks not minutes.

If you haven’t noticed the moon is in different phases and also possible captured during different times of the day.

So you’ll always get something that looks like this https://astronomy.stackexchange.com/questions/36657/how-to-e...

He must have re-pointed the camera between exposures of the moon. In the article, he says that because of a camera malfunction, he had to capture a shorter interval than originally intended. He did this without changing the template he had put into the camera's viewfinder.

https://www.timeanddate.com/eclipse/in/australia/sydney?iso=... has the direction and altitude for the moon as viewed from Sydney during the eclipse. I suspect that if plotted out, they'd trace out something pretty close to a straight line.

Printed template, multiple exposures. There are images of the template around middle of TFA.

If you continue watching the moon's position in the sky through full lunar months, the path is sinusoidal.