One thing that threw up a warning flag in the article was this sentence:

I suggest that the true source of macroevolutionary change lies in the non-linear, or chaotic, dynamics of the relationship between genotype and phenotype - the actual organism and all its traits.

My understanding is that chaotic dynamical systems are just a subset of nonlinear dynamical systems, so the whole title seems sensational and as if the author just used "chaos" not because he has reason to believe that evolution is actually chaotic, but instead because chaos sounds really cool.

If we simply restrict the theory to evolution being nonlinear, that's almost certainly true. Why would evolution be linear? To paraphrase Stanislaw Ulam, talking about "non-linear dynamics" is like talking about "non-elephant zoology."

The author does support the chaos hypothesis later on in the article by talking about the tree of life being fractal, but I'm definitely going to need more evidence than a single paragraph without references.