"history offers no examples of a society that has demonstrated sustained material advance in the face of long-term population decline"
Of course it does: Russia, from 1999-2007. For most of the last decade, Russia was the fastest growing economy in the G8. And it may have been growing even longer than that if you discount the contribution of the sudden drop in weapons production after the fall of the Soviet Union.
And second, how much of the cumulative growth from 1999-2007 was due to astronomical energy prices? I don't think it's absurd to point out that for half of the period you mention, energy prices made Russia's economy appear much stronger than it was in reality. The same happened in the late 1970s and the early 1980s with the USSR. Many attribute the USSR's implosion in large part to the collapse in energy prices in the late 1980s/early 1990s, since the failings of their centrally planned economy couldn't be concealed any longer.
Not when the thesis on the table is that "relentless, unremitting, and perhaps unstoppable depopulation" is "a bomb" that "amounts to an ethnic self-cleansing" and "carries with it grim and potentially disastrous implications." Since depopulation began in 1992 Russia has enjoyed eight years of extraordinary economic growth, not all of which can be accounted for by rising oil prices. That is a salient fact, which the article completely ignores. At best it's shoddy journalism.