I feel like comparing Rome, Great Britain, and Spain to Facebook, Apple, and Google is like comparing to apples and oranges. They have nothing in common other than the fact that they're big. The empires fell because they're trying to force a common lifestyle over a large group of people. When you try ruling over people against their will, then the resistance from the people eventually leads to the collapse of the empire (I'm oversimplifying, but still...).
Google, Facebook, and Apple, on the other hand, don't try to force anything on anyone. They offer a service, and people decide to use it.
The comparison to Ford, Microsoft, and Kodak is perhaps more apt, but really only works well when compared to Apple. Ford stopped being a superpower because so much competition arose in the auto industry. I think in the end, Apple will face a similar situation.
Facebook, Google, and Amazon, however, are completely different than anything the article has discussed. All three of them are based pretty much completely on the internet. I think that creates a completely different dynamic that we probably don't actually know too much about because the internet hasn't really been around that long (relatively).
I don't think Google or Amazon will be falling any time soon. Survival on the internet seems to depend on adaptability to meet the needs of the consumers, and both Google and Amazon seem very adept at keeping up with what we need. Both provide a rather large range of services, and they also do it extremely well. Unless a company can be more all-encompassing and perform better than Amazon or Google, then people won't want to switch.
That being said, I do think Facebook will be the first to go. It only does social media - Amazon and Google on the other hand both have their fingers in a ton of pies. Facebook provides only one service, and not particularly well anymore. I think the primary reason people still use it is because everyone's on it. Why switch to a different social media network when nobody else has yet?