Does it, or does it merely speculate that such has occured in animals? The duplication of genes is (according to the article) far from random. Maybe genes that get expressed the most or tend to mutate the most have the most copies. That is engineering and it does not demand a naturalistic explanation.
The article assumes that gene duplication will automatically produce an increase in complexity. There is little evidence that this is true. The reason is that there is precious little evidence that gene copies can ever become a gene with a function much different from the old gene. Because of that, all the duplications in the world won't get you from ameoba to man. It will just get you to a man with a lot of psuedogenes. We have lots of such genes, but so much "junk DNA" is conserved that some have been led to wonder if it does not have a function after all, such as steering protiens to the right part of the cell.
The author is not speaking to the distribution of duplication events before selection. From our POV that is still random. We don't know initial conditions, don't know a mechanism, and can't predict future events. That's as random as things get.
What it comes down to is that nobody can distinguish between a random and an "intelligent design" event.