Someone once defined history as "Argument from the past." I think it is worth noting that all perspectives are incomplete. Tainter does talk about why the Eastern Empire survived longer but another interesting perspective on that (and one more relevant to the article) was put forth by Herwig Wolfram in his book "The Roman Empire and Its Germanic Peoples."
Wolfram points out that before the Migration Age began in earnest, the Eastern Empire was spending more in the military (and that was only 30% of the budget) than the Western Empire was collecting in taxes, and the issue was, in the West, that the Senatorial families had achieved such a monopoly on wealth and power that they both couldn't be effectively taxed and controlled the economy. Some families had a budget that was as high as a third of the whole Western Empire's budget (suggesting it is likely that some families had businesses which were consuming more than the Western Roman military). According to Wolfram, this was not the same in the East.
Nonetheless, the East found its military too expensive during the Arab wars and that's where the Theme System came from.
The perspectives of Tainter and Wolfram are not unrelated. Complexity usually does concentrate power and resources in coordinator roles, and that concentration itself cannot be maintained without complexity -- remember that the fall of Rome effectively meant the transition of the role of slave into a role of peasant simply because central enforcement of slavery could no longer really occur. But at the same time the Ostrogoths could not challenge the powerful families enough to hold Italy for more than a couple of centuries before the Eastern Empire invaded and the Goths fell for the same reasons (according to Wolfram) that the Romans did.
Regarding the article, one of the problems not discussed is the issue of economic concentration. These breakthroughs usually demand that. The industrial revolution wasn't caused by population, but by concentration of economic power in a few hands and the quite intentional efforts to evict peasants from their lands and make them destitute factory workers.