These to me sound like Arcologies These Theoretical structures are designed to place a large population in a vertical structure rather then spreading it out horizontal. Also note that if you assume 1000 people per square mile your not accounting for production centers, food vats and the complex ventilation systems described in the book. all of that has to fit in the 2 mile width. I also get the impression that they are walking on "open" streets. meaning that the space is set up to mimic being out side despite the fact there is a ceiling.  I'd wager that only about 75% of the Spire's Volume is usable for habitaion.