I wonder if the primary purpose of the law was to have a catch-all charge to file against people who stole military equipment? Of course there are charges like espionage and theft, but it seems like it could be a tactic to be able to levy "exporting an encryption device" charges in addition to everything else.

It was a legacy from the era of the enigma machine, where encryption required a dedicated cipher device, rather than something you could do in pure code.