The clip doesn't show it, but Burke in the documentary makes the same connection as the article, but in a little more detail. He goes from Jacquard -> Babbage -> Hollering ( who used punchcards for the 1890 census), who founded the company which later became IBM.
Really fascinating to watch Burke pull up existing pieces of the modern world and examine their roots. Most of the time, it reveals that most revolutionary innovation was just a variation/consolidation of existing technologies.