So this question is really too broad to answer conclusively here. There are sections on the FAQ on many of these topics. For example, this entry covers the decline of the Roman Empire, and I've answered questions about the Maya collapse here, and here.

However, I would suggest that you repost this in /r/AskAnthropology. That sub is more well suited to these kinds of "big picture" questions involving cross-cultural comparisons. You'll likely generate better discussion there. Based on what I've read on this article, I would say that nothing in it is especially new. These kinds of explanations have existed for a while, and while they are in part correct, the issue is more complicated.

Take for example the assertion that civilizations collapse when they exhaust their resources by hitting the ecological carrying capacity of an ecosystem. While you can find plenty of evidence that supports this position in the academic literature, part of it is due to a bias in how archaeological data is collected. Lets say, hypothetically, you're an archaeologist studying an ancient city in southeast Asia. Through excavations you uncover evidence of a rapid abandonment of public buildings and a gradual decline in overall population dating to around 600 AD. You're not quite sure what caused this, but you have a hunch. You send some of your archaeologists out to excavate some agricultural terraces in nearby hillsides and you take some sediment cores from a nearby lakeshore. Your excavators find evidence of a major erosion event on the terraces dating to about 600 AD, and the paleoecologist studying the sediment cores comes back with evidence for a major ecological shift about this time. C4 pathway plants (grasses, mostly) are replaced by C3 pathway plants (like trees), which suggests that the farmland was slowly replaced by forest.

So now you've solved the problem right? The city collapsed when their agricultural infrastructure broke down and they lost the ability to feed themselves. Then the farmland reverted to forest. Well.... no. Not exactly. All you have is a correlation between an ecological event and a social collapse. That doesn't necessarily say that the ecological event caused the collapse. The society could have collapsed for unrelated reasons, and then they stopped maintaining their agricultural infrastructure which caused the ecological change. The problem is that it's relatively easy to see environmental changes in the archaeological record when compared to social causes. So one can easily jump to conclusions that tie environmental factors to social events. This kind of explanation also assumes that the environment has some kind of "normal" carrying capacity that humans are supposed to operate at, and that when we exceed this we break the system. That's kind of a bad way to understand the relationship between humans and the environment, since both us and the environment are constantly changing and "negotiating" with each other. You might also want to check out this article by Clark Erickson, which explains some of the problems with this line of thinking as it applies to the Tiwanaku civilization.

Another problem exists with claiming that inequality leads to collapse of civilizations. The issue is that economic inequality is very much part of how we define what a civilization is. See for example Gordon Childe's checklist of civilization. Notice how numbers 2, 3, and 5 are all based around the existence of some kind of economic inequality. So, if economic inequality is part of how we define "civilization," then the collapse of a civilization is, in part, defined by a reduction in economic inequality. So when you say "collapse of civilizations is caused by economic inequality," you're also kind of saying "a decrease in economic inequality is caused by economic inequality." And you can see how that becomes rather confusing rather quickly.

The study based on the HANDY model has been accepted for publication in the peer-reviewed Elsevier journal, Ecological Economics.

Published in scientific journals but not historical ones? A team of mathematicians, biologists and physicists but no historians or archaeologists? Shocking!

This is nothing but Malthus: 2014 Edition, minus the subtleties, nuance, intellectual rigor or value to economic studies. Based on what I can see from a few minutes of Googling, it is a pretty textbook case of assuming the premise: the collapse of these empires comes from this stew of factors, so we make a model that shows these factors caused the collapse, and lo and behold, those are the factors that caused the empires to collapse. The sky is falling!

There is no TL;DR, and scholars have been debating on what caused the Roman Empire to collapse in the West for two hundred years (longer, really), and saying it was caused by elite disparities or environmental collapse is enormously controversial (and not really widely accepted anymore). Even if there was a collapse is controversial. And Rome is by far the best understood "collapse", and saying that a particular factor is "clearly apparent" in the case of the Maya is almost comical.

If you want an interesting take on collapse and development, and what we can learn about it today, try Ian Morris' Why the West Rules: For Now. He essentially argues that "collapses" happen because of factors that built up during the case of the rise, but he does it with a great deal of nuance and an eye towards specifics.