RFID Based Listening Device
It seems likely from inspection of diagrams and photos of the device that the cavity was resonated in conjunction with a coupled external 1/4 wave whip - although that is not what is said in the text accompanying the diagram below. Text and photo from here   

They say


It was simply a resonate chamber, with a flexible front wall that acted as a diaphragm, changing the dimensions of the chamber when sound waves struck it. It had no power pack of its own, no wires that could be discovered, no batteries to wear out. An ultra-high frequency signal beamed to it from a van parked near the building was reflected from the bug, after being modulated by sound waves from conversations striking the bug's diaphragm.




Photo of "The Thing" here from this website 



This gives a clearer picture. The cavity is a high Q resonant cavity tuned to the frequency of the whip. Details of design of such cavities can be had in the various ARRL and RSGB amateur handbooks or via various on web papers and calculators



Two photos below from "Spybusters" here

 





Cavity resonator design:

Useful paper. Bell Labs 1946 !!!
High Q Resonant cavity for microwave testing

Masters thesis. 2010
Design of a Cylindrical Cavity Resonator for 
Measurements of Electrical Properties of 
Dielectric Materials 


CERN? 1995?
Resonant Cavity Design Using the Finite Element Method

Wikipedia - "Thing"