First off, two of their "studies" simply compared the hamburger icon to different types of icons, but the functionality remained the same (slide out). Only one looked at changing the navigation entirely.

Second, this is not so much a reflection of fly-out/slide-out navigations as it is a reflection of the fact that on mobile you just have less screen real estate period. Nowhere in that article is there a real reckoning with that fact.

I've yet to be convinced that fly-out/slide-out/hamburger navigations are worse than the alternative when you have lots of items to display. Either way you're not going to be displaying something, and whatever is not immediately visible will receive reduced engagement. If your home page/screen is full of navigation items, something else will be hidden instead.

Not to mention the article provides solution for cases that have many navigation items - something that is very common.