I don't believe this recording has ever been mentioned on ATC. The complete original film soundtrack performance of the On the Waterfront score was long thought to be lost (even by Bernstein himself). However, the scoring session masters did surface a few years ago and Intrada released the soundtrack on CD. For the '54 recording sessions Morris Stoloff conducted and Bernstein was on the piano for one of the tracks. Bernstein also wrote all of the cue and track titles.
When you listen to Bernstein's score unencumbered by dialog and sound effects, it is possible to recognize little music "quotes" which hint at themes that would be more fully developed in his West Side Story score.