Thematically, it makes a case for complexity not being important to software development. I disagree, but stipulating that the author is correct, where does that slippery slope end? Virtually no formalized CS knowledge is required to make expert use of Microsoft Excel, which is itself an extremely important programming environment. What parts of CS does this analysis include in the requirements for development? Is it important to know how a hash function works if your language gives you a dictionary ADT? Is it important to understand the memory hierarchy if you're just shuttling things into and out of an SQL database? There's a rather large population of "Rails programmers" and "PHP programmers" that need know very little more than an "HTML programmer" does to get their job done.
But it's the specifics of the argument that really bug me. The author seems to be making a case that even if you understand complexity, it's hard to deploy it in a real application. That idea seems totally alien to me. I don't routinely analyze the complexity of a sort or a shortest-paths graph reduction, but I certainly feel like I benefit from understanding how the typical algorithms used to solve those problems scale with the size of their inputs. Simpler: any time you select a binary tree instead of a hash table for your lookup table because you realize you need range queries or sorted traversal, aren't you leaning on complexity theory?