A local lawyer, R. Raleigh D’Adamo, was the winner of that 1964 contest. His design separated local from express routes and assigned separate colors to each of them. Submissions had to fit all the subway lines into a geographically correct map. So to use as little space as possible, D’Adamo employed colored squares along shared lines.
Personally, I would’ve found the map tough to use as a tourist, none of the station names are indicated. It was replaced by Massimo Vignelli’s version three years later.