Effectively, the building code they are talking about the value of changing. Fully enclosed stairways at the back for each "slice" would be cost prohibitive, and exterior "fire escape" type stairs are not allowed either.
It's definitely not the densest design possible, but it certainly seemed to let them fit a lot of fairly spacious 1-2 BRs in not a lot of space back in the early 20th c., and the height can scale up pretty well (though the elevator probably becomes at least a soft requirement above 4-5 floors).