The article in question makes the claim that the modern Democratic World is approaching it's downfall (unless it drastically changes it's course), and it does so by citing the works of some experts who happen to make the comparison between our world and that of the Roman Empire.
I'm obviously not interested in answers addressing the claims about today's world.
Here's the relevant passage:
The past can also provide hints for how the future might play out. Take, for example, the rise and fall of the Roman Empire. By the end of the 100BC the Romans had spread across the Mediterranean, to the places most easily accessed by sea. They should have stopped there, but things were going well and they felt empowered to expand to new frontiers by land. While transportation by sea was economical, however, transportation across land was slow and expensive. All the while, they were overextending themselves and running up costs. The Empire managed to remain stable in the ensuing centuries, but repercussions for spreading themselves too thin caught up with them in the 3rd Century, which was plagued by civil war and invasions. The Empire tried to maintain its core lands, even as the army ate up its budget and inflation climbed ever higher as the government debased its silver currency to try to cover its mounting expenses. While some scholars cite the beginning of collapse as the year 410, when the invading Visigoths sacked the capital, that dramatic event was made possible by a downward spiral spanning more than a century. [...] By the 3rd Century, Rome was increasingly adding new things – an army double the size, a cavalry, subdivided provinces that each needed their own bureaucracies, courts and defences – just to maintain its status quo and keep from sliding backwards. Eventually, it could no longer afford to prop up those heightened complexities. It was fiscal weakness, not war, that did the Empire in.
The question of why the Empire fell is probably the most commonly asked question about Rome on this subreddit.
Quality answers can be found in this section of our FAQ, most notably in this answer by /u/LegalAction.
tl;dr: To blame the fall of Rome on a single factor would be an oversimplification. This particular theory is similar (but not identical to) Edward Gibbon's theory of moral degradation and corruption in his Decline and Fall of the Roman Empire, a fairly biased and outdated book I would personally read more to understand liberalism in the 18th century than I would to find information on late antiquity.