The original research report did not say anything about "an impending bird apocalypse." It is the Slate article that used that term, as a pejorative for the Cornell Bird report.
It is Slate's interpretation of Brian McGill's Dynamic Ecology blog that "While that loss in biomass is concerning, he argues, it does not necessarily suggest a looming extinction event." The Cornell paper in Science did not suggest "a looming extinction event."
Most importantly, human biomass in the U.S. has increased from 205 million to 330 million in the same period. More humans (and their domesticated food animals and pets), less wildlife. Fact.