In terms of timing, the author/ speaker had no way to know this, but at the time they're saying hey, actually this is practical because you don't need a machine (1941), both sides are in fact using machines.
The Japanese begin using "Purple" about this time (prior systems "Red" and "Blue" were not mechanical), the Nazis had Engima even before the war and have also been using Lorenz / "Tunny" for a few months although only in prototype and their Allied counterparts are using a roughly similar technology to Enigma (Typex) and another weird (but pragmatic) rotor machine the ECM Mark II.
I think the GP misinterprets that bit in the paper and the assumption the author was unaware of the existence of electromechanical cryptographic machines is inaccurate. He’s arguing practical cryptography can be done without machines.
I agree that the author is arguing you can do that. But he's wrong, you can't, it's monstrously difficult for a human to do what the machine does easily (yes I'm aware there's a flawed modern attempt described in the novel Cryptonomicon) and given the human propensity to fuck things up it's just futile.
The War provided an excellent proof by fire, it's more obvious for Japan because they weren't using machines at the start at all, and so we broke literally everything. All "secret" radio communication by the Japanese was decoded, translated and handled as intelligence up until Purple (a machine) was introduced and then it got harder.
The Japanese begin using "Purple" about this time (prior systems "Red" and "Blue" were not mechanical), the Nazis had Engima even before the war and have also been using Lorenz / "Tunny" for a few months although only in prototype and their Allied counterparts are using a roughly similar technology to Enigma (Typex) and another weird (but pragmatic) rotor machine the ECM Mark II.