Take a look at the sentence again:
Neither the unhappy
man with the cold soup nor
the irate woman with an empty glass of iced tea
could get Gloria’s attention, for this waitress was too busy flirting with
Jose.
When you use neither ... nor, you must maintain parallel structure. Since the unhappy man with the cold soup, a noun phrase modified by a prepositional phrase, follows neither, the same construction must also follow nor. The irate woman with an empty glass of iced tea qualifies, so the sentence is parallel.