These babies had a carriage/cross slide and a sliding tailstock with a rotating turret. So X and Z are likely the carriage, and his A is sliding the tailstock (done with a big ol' handle originally, move forward, move back, rotate, slide forward again with the next tool). Not sure how he'd handle rotating the turret to its positions and knowing tool lengths, but I'm sure it can be done:)
These things preceded CNC lathes for production type work back in the day!! Pretty cool in 1945! Right in there with VTL's and gear shapers.