Just to make a point clear that the author seems to not account for, Darwin himself hypothesized that organisms should be equally likely to become increasingly or decreasingly complex at any point in history, but that average complexity would always tend to increase, because there is a lower limit on how complex an organism can be, while an upper limit seems to not exist. Again, this was hypothesized 150 years ago (one need only observe a cave dwelling salamander without eyes to know this). All the bullshit about increasing complexity being the natural order of things is the quasi-religious interpretation of evolution. Every biologist worth his salt already knows this, but for some reason, this is how it's taught in school.
On the subject of genetics, it was a surprise to learn that the number of genes doesn't correlate to morphologic complexity. However, even that isn't the whole story. There are a such thing as non-coding RNAs (which happens to be my field of study), and among those specific types of genes, there is a strong correlation between number and complexity. These genes exist to regulate expression of proteins, and they do so by direct binding between RNA strands. So it turns out that what has evolved to become vastly more complex is the regulatory machinery that each cell carries. And it makes sense, too. The number of genes is linear, but the ways in which genes interact with other genes is non-linear. Therefore, it's the non-linearity introduced by RNA-RNA interaction that seems to produce complexity. Fascinating field, really, but of course I think that, as it's my livelihood.