Even computer programmers who spent the majority of their working output working alone can benefit a lot from having good connections when it comes to finding good jobs.
People skills have great value for programmers, and finding jobs is a very small part of it. I write this from personal experience.
Programmers are still people. The amount of great software any one person can write in their lifetime is very limited. Teaching or convincing others (from coworkers to the rest of the world) to agree with you on what makes software great, to write great software themselves, and to use it, are the greatest force multipliers any programmer can have, just like in most other fields.
Sometimes there are exceptions; one may invent a new algorithm or write some new software that everyone agrees is great. But most of the time you have to convince people - not just less-technical managers making purchasing decisions, but other programmers who don't think that global mutable state is a problem, really, it worked fine in my grandfather's time and it's good enough for me.
People skills have great value for programmers
Yes, but we didn't disagree on the value of people skills but on the other value social interaction outside of work. You are mostly convincing your coworkers while you are at work and not a social hangouts.
Convincing the rest of the world to adopt programming technique X is more likely done via the internet then through social hangouts.