The author conflates networking with shameless self-shilling. This makes for a pretty thin strawman.
Networking, in the sense of maintaining strong professional relationships and having a presence at professional events, creates a strong passive upwards pressure for someone who is talented. If you "spring to mind" as someone I can trust to "do X," or if you spring into the mind of the person I task with finding someone to "do X," then you are that much more likely to be offered the opportunity to "do X".
You may find the same kinds of "do X" opportunities through other means, but as X becomes increasingly specialized and requires more trust, networking becomes more and more important. For example, I can mass broadcast an ad for entry-level Java developers. I cannot do that to find a systems architect to design a high uptime, low latency, massive throughout web service. I'm likely to go to a short list for the latter and avoid interviews completely, if at all possible.
Obviously accomplishments are important. Accomplishment one of the foundations of a strong professional identity. Without evidence of your abilities, networking won't put you on anyone's short list. That's a catch-22, and you also need luck and the ability to inspire someone to take a chance on you to get your foot in the door. Both of those are improved dramatically by networking.