The programming languages that will best survive the apocalypse are the ones that can run on chips that best survive the apocalypse! I think that there're be a big turn toward highly-efficient compiled languages: Rust and Go are well-positioned for this, C will still be around, but languages like PHP and Ruby are very poorly suited for this. Anything that can be adapted to run on a microcontroller that you can scavenge from old cars that no longer can get gas will be in high demand.
I also think we'll see a turn toward more local production of semiconductors, which may require moving back in process nodes toward older technology where the supply chain and manufacturing process isn't as complex.
I don't think backwards-compatibility is as important as the author thinks it is. Enough other things are going to break in the economy that people will be willing to make due with software that gives them basic communication & computation abilities even if it doesn't have all the bells and whistles of modern software, particularly if modern software becomes completely unavailable due to infrastructure failures like cable lines coming down and there not being enough power to run datacenters.
Final thoughts: I think distributed technologies like mesh networks, data synchronization algorithms, networking, (proof-of-stake/storage) blockchains, etc. will become significantly more important. I wouldn't count on the cloud surviving: it has a lot of physical infrastructure dependencies, and physical infrastructure is already crumbling. Software that you can run locally on a device and communicate over unreliable networks will become very important.