It was reportedly designed by a couple of Westingouse Research Lab employees † "during a long lunch hour", though improved, and actually built, by engineers at its Pittsbugh plant.
The Nimatron was not the giant robot used as an illustration on some web pages! This was actually Elektro, the "amazing Westinghouse Moto-Man", in the same pavilion. [The Christmas 08/09 issue of NewScientist had an interesting article on Elektro's story. [Apparently this article now needs a login — sorry...] That article also mentions a YouTube video of Elektro performing at the World's Fair]
† It turns out that one of those 'employees' (and the originator of the idea) was Ed Condon! He later was a prominent physicist, and may be best known for chairing the 1968 government investigation into the UFO phenomenon. His own recollection of how the Nimatron came to be is recorded here. (The relevant section is way down in the text — search for 'Nimitron' [sic... this is an oral transcript!]) He apparently considered it his "biggest failure", because he didn't think of digital logic as more than a toy!
The device was actually patented by Westinghouse, under Condon's name (as well as the two engineers who actually built it). Search for US Patent 2,215,544.
Image reproduced, under Fair Use Copyright provisions, from
The American Mathematical Monthly vol 49 (1942).
[Sorry about the quality of reproduction, but this is the only actual photo of the machine I've been able to find.]