Also to note, the paper is titled "Managing the Development of Large Software Systems."
The author outlines 5 steps they believe need to be used to improve the success of a project. One step is called "do it twice" in which the author advocates the development of a prototype well in advance of delivering the final product. I think this is iteration. It's not indefinite iteration, but it's definitely not showing the big bang single release waterfall approach either.
It also advocates to involve the customer throughout the process instead of only at the end.
The summary says to refer to Figure 10 as the process that incorporates the author's steps. This final diagram is pretty far from the simplified and flawed waterfall picture that has been pulled from the front of the document.
[1] http://www-scf.usc.edu/~csci201/lectures/Lecture11/royce1970...
Can you specify which book/process/document(s) you are using in your day-to-day? This could be very interesting in future discussions with clients, to say the least!