> These political divisions are arbitrary anyway.
Not sure how interstate activity and travel is regulated/limited in China (in normal times), but in the U.S., state borders are not just some imaginary political construct. Laws and services – and therefore, impact to respective populations – can drastically differ by state lines, and ignoring that is a huge mistake.
You should be concerned about the fraction of land area on which you are at high risk. If 100 people have it, and each person creates a high risk across A area (and the areas don't overlap), that is 100*A / country-area. Which is proportional to cases/area (presuming A is constant) the first statistic he used.
EDIT: if you know you are going to interact with N people, the cases per population figure is relevant again.
It's that the case anywhere? Even city centre / suburbs will have different values, much less a whole province where A may contain an empty field or a group of residential buildings with 50 floors and shared lifts.
I could see how it would be useful for a map of a city, or maybe even at a scale of some regions... but not for comparing totals between regions.