I don't understand neither the author's nor yours approach to doing this in Illustrator.

If you want to have a square inset into a circle in Affinity Designer, you:

- Draw a circle.

- Create a square from the middle of the circle outwards. The square will _constraint_ perfectly to the circle.

If you want to do the reverse (circle inside square), it's even easier since the bounding box of the 2 objects is one and the same ...

I have the feeling that the author is simply unfamiliar with current design programs. Those haven't stagnated like one might think from the article.