You'll note the cruciform shape, right away. Most classically designed churches maintain that in one fashion or another (even though it might not be immediately apparent).
Without going into a bunch of detail that you may or may not be interested in, the function of each of the areas somewhat parallel the different areas in the temple in Jerusalem. You can also trace some of this in Rev 5 - 7 as well.
A lot of tradition goes into that, obviously. The evangelical mode of worship simplifies much of that away and the sanctuary becomes an auditorium. Communion is usually passed around to the congregation rather than done at the altar (though the latter is a means that Lutheran churches, which kept more of the Catholic feel than others did, still use).
I know about St. Pet’s because I used to live in that area and when your author said there was only one Catholic church he knew about that looked like St. Martin’s, I wonder if it was St. Pet’s. Externally it has the St. Martin’s decor which is what your author was talking about, internally (as a Wascally Evangelical I never visited it, though I rode past it many a time on the way to the church I did worship at) I guess it looks like your picture.