I have created academic work both in LaTex and in Word and while I have not measured it in an objective way I also had the feeling that LaTeX could create better looking results once you've got over the first hump.
On the other hand, the integrated nature of a system like Word were spellchecking, annotations etc. are all part of the main tool you work with makes it very effective. It takes pretty long however to develop a workflow that avoids all the pitfalls.
In a sense, LaTex makes you believe that once you got over the initial hump, you have typesetting super powers but you will miss out on some of the integrated UI stuff that may boost productivity. Word on the other hand makes you believe that you already know everything while you still need to keep fine-tuning your workflow until you don't mess up constantly.
They didn't measure the quality of the typesetting in any fashion, though, which is what the GP's claim was about; they measured the rate of errors typists made under time pressure.
It's also unclear what LaTeX software they used, since the one I use has integrated spellcheck, etc.
That's a hugely important point and in a way it shows that they are comparing apples and oranges. Word is a complete document editing system (well, more or less) while LaTeX is a type setting systems and you need additional tools to use it. Those tools can range from a simple plain-text editor (say, nano) to totally integrated environments that are similar to word in their feature set.
As it turns out since the authors' fee was per-copy, while the typesetters' fee was a one shot deal, they made much more as typesetters (though this situation might get reversed if the book keeps selling for decades…).
My experience with LaTeX is that it enables and encourages my OCD behavior and it is very easy to be sucked into an enormous game of package dependency hell and whack-a-mole to achieve some desired aesthetic result. Whereas with Word I already expect an inferior result so I'm somehow more easily happy getting 95% of the way there and calling it a day. It's not too hard to learn "what not to do" in Word and how to use counters and references. Certainly if you've got the capacity to learn LaTeX, you can learn how to markup Word properly and use styles etc.