This article is typical of many that claim proven limits on the feasibility (or, in this case, the capabilities) of generalized artificial intelligence, in that it structures the argument in a way designed to avoid discussion of the issue.
It starts by claiming that there is no such thing as general intelligence. What specialized intelligence, then, is human intelligence? It's specialized for "being human". The author is apparently unaware that this tautological response eliminates the distinction between general and specialized intelligence, as one could just as validly (or vacuously) say that a superhuman intelligence is specialized in being what it is and doing what it does. The author has invalidated the hook on which he had hung his argument.
A lot of column-inches are expended on repeatedly restating that animal intelligences have co-evolved with their sensorimotor systems, which is a contingent fact of history, not a fundamental necessity for intelligence (as far as we know; but then the whole article is predicated on the feasibility of AI.) He raises the 'brain in a vat' trope, but no-one is suggesting that AIs must be disconnected from the external world. Furthermore, this line of argument ignores the fact that many of the greatest achievements of human intelligence have come from contemplating abstract ideas.
When the author writes "most of our intelligence is not in our brain, it is externalized as our civilization", he is confusing the achievements of intelligent agents for intelligence itself. When he writes that "an individual brain cannot implement recursive intelligence augmentation" he is confusing a limit on human capabilities for a fundamental limit on intelligence itself...
I am far from convinced that the singularity must follow from achieving human-level artificial intelligence, as we don't know how to get to the starting line, let alone know how the problem of bootstrapping intelligence scales, but the arguments presented here do nothing to persuade me that it is impossible.