a mile-high skyscraper that never got built.
The game show connection is the would-be architect, Frank Lloyd Wright. He was a pioneering media manipulator, taking to television in the 1950s to appear on the popular game show What's My Line. (His profession, the home audience learned, was "World Famous Architect.")
As it happens, the essential WML channel on YouTube has preserved Mr. Wright's turn on the show. He was 88 years old at the time and that created a few problems, but he managed well enough, thank you. The panel guessed him quickly and Mr. Wright complimented them as "extraordinarily intelligent." He was rather critical of the studio's acoustics, though.
One more note: this was one of the few times that the ladies on the panel - Dorothy Kilgallen and Arlene Francis that night - stood to shake hands with a guest. By 1956 Frank Lloyd Wright was a living legend and merited such special treatment.