Then make yourself worth being connected to. It doesn't have to be in a "the person who does X" way. It can be as simple as the person people want to take a coffee break with, or the person you want to go for beers with, or the person you ask to help when you move!
I'd disagree with this. Otherwise what good are you if you aren't "the person who does X?"
Is there someone out there who thousands of people explicitly only want to take a coffee break with? I mean I want to have a coffee break with a lot of people, but not cause they are good coffee drinkers, but because they have made significant progress in some thing I care about.
The two things you describe as the core of what people are are effectively a therapist (the person who [communicates]) and a moving company (the person who [you ask to help when moving]) respectively. Otherwise those are just regular friends...not "connections." Outside of the scope of this article.
Consider that most of your indirect colleagues are not well-versed enough to know whether you're doing your job well or not in the first place.
Why are so many clowns in positions with high rank, and so many better-qualified people are further down the totem pole? Because people don't respond naturally to qualifications. They respond to getting their personal interests and desires satisfied.
If you present a credible professional front and you are well-liked, that's all that matters, and you will be well-connected and rewarded well outside of any rational proportion.
Of course a very bright engineer will naturally achieve some success, but there will always be a bar limiting his growth to how much people who can open new doors want him around and trust (in a very personal sense) him.
Soft skills are real, they are skills and they have have value in both in professional and personal settings.