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.
You make a good point. What is an equal-area, tessellated shape that could be used in its place? I guess a triangle. Or one of these: https://upload.wikimedia.org/wikipedia/commons/thumb/6/67/Sp... https://upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Sp...
For just shapes the above is a nice visual start.
However a striking feature of the linked article is how frequently there's a major city right near a cell edge.
A more useful list might be constructed by some process involving assigning a "city" an imprint size based on population, and a surrounding 'metro area' based on absorbing any weaker cities that overlap until the process either repeats or is matched by a neighboring city.
A starting point for results that are already similar to that: https://en.wikipedia.org/wiki/Metropolitan_area
The US specific list: https://en.wikipedia.org/wiki/List_of_metropolitan_statistic...