Machine rooms of the era had perhaps dozens of rack-mount sound players/recorders that used "full-coat" 35mm film coated with magnetic oxide (just like traditional mag tape). These machines were driven from "house sync" 3-phase AC power which was synchronized to the projector to keep all the source tracks (dialog,, music,, FX, etc.) in sync with the picture.
Ref:
https://en.wikipedia.org/wiki/Sound_follower
Studios had "mixing theatres" which were set up with a large screen and projector (like conventional exhibition theaters) , many with seats for audience. But they had a large mixing console/desk in the middle of the audience area where the final mix could be executed (and "re-recorded") in "real-time" while watching the picture on the big screen.
Ref:
https://en.wikipedia.org/wiki/Re-recording_mixer
I attended a pre-release screening of "Star Wars" (the original Episode 4) in the big mixing theater on the 20th Century Fox lot in Century City. The sound was spectacular from Darryl F. Zanuck's special overstuffed easy-chair in the center of the theater. The sight of a room full of 35mm sound recorders all starting and stopping in sync was pretty impressive also.