I think that's inevitable with or without LLMs in the mix. I also think the industry as a whole will be better for it.
The documentary he's referring to is likely "Farewell, Etaoin Shrdlu," released in 1980. It chronicles the last day of hot metal typesetting at The New York Times before they transitioned to newer technology. The title comes from the nonsense phrase "etaoin shrdlu," which appeared frequently in Linotype machine errors due to the way the keys were arranged. The documentary provides a fascinating look at the end of an era in newspaper production.
So same programmer with the same 8h of workday will be able to output more value.
Some will undoubtably transition to broader based business consultancy services. For those unable or unwilling to do so the future is bleak.
There is an old documentary of the final days of typesetters for newspapers. These were the (very skilled) people who rapidly put each individual carved steel character block into the printing frame in order print thousands of page copies. Many were incredulous that a machine could ever replicate their work.
I don't think programmers are going to go away, but I do think those juicy salaries and compensation packages will.