I quibble with the description of the shapes bounded by 10 degrees of longitude and latitude as "rectangles" - they're not even planar shapes, and their adjacent sides certainly aren't at right angles. Some of them don't even have four sides. This bears considering when looking at the map, because some of those regions are much, much smaller than others.
He's not making a mathematical definition of the areas. 'area' or 'box' is a simple description that everyone can understand. And the map projection used does form squares.
Some of those squares have zero-length edges.