Is the author perhaps thinking of something more like "history of philosophy"?
What you say about philosophy being more like mathematics is true, and as far as I can see, going forward philosophy is just philosophy, and it would be silly to label it with nations and cultures.
But looking backwards, the path that brought different cultures to the table, that got them thinking about the nature of things, is quite different. Labeling those different paths according to the cultures that developed them makes sense, and might be a very interesting study. But that's not philosophy as such, it's a discussion about philosophy.
What you say about philosophy being more like mathematics is true, and as far as I can see, going forward philosophy is just philosophy, and it would be silly to label it with nations and cultures.
But looking backwards, the path that brought different cultures to the table, that got them thinking about the nature of things, is quite different. Labeling those different paths according to the cultures that developed them makes sense, and might be a very interesting study. But that's not philosophy as such, it's a discussion about philosophy.