In this brief quote, the author Joe Celko is using a figure of speech, specifically syndecdoche, in his explanation of how the punched-card framework shaped data processing, from the turn of the century up until the early 1970's.
In syndecdoche, "part of something is used to refer to the whole thing". In this case the "part" is a punch card, and the "whole" encompasses punched-card data processing equipment and methods based on that kind of equipment.
Conceivably one could regard the figure of speech as an instance of metonymy, in which "a thing is called ... by the name of something intimately associated with that thing or concept." That is, "The punch card was data processing back then" may be seen as referring to all the keypunches, sorters, and other card-based unit record equipment and computers by reference to the pieces of paper they all processed.