I have yet to see one comparison to the fall of Rome that wasn't complete horse shit - and this is no exception. It's just madness from the beginning - "Rome" began to fall as soon as it was relevant, it lasted for more than a millenium, and if you just pick the right point in time, you can make an argument for almost anything.
Except in this case the author didn't even bother to pick the right time, instead opting for some quote "A few centuries" before the "rapid" descent. Most empires last only a few decades.