I've spent a lot of time living around wild cats, and I've yet to see a cat hunt a bird. Of course cats do hunt birds, but I'm very curious about how these figures are reached, in this case, how reliable those isotope studies are.
Another anecdote - my cat was 100% indoor first 6-8 month I had him. Then I started to let him outside during day and he started immediately to try to hunt. His first attempts were hilarious, like trying to hide just by laying down and flap around with his tail from excitement, birds would look funny at him and just casually jump away if he got too close. He also wore a bell all of the time, which made it even more impossible. But after half a year he started to consistently kill 1-3 animals per season, birds and mice. One time he killed a huge pigeon. And thats only the kills I know of, since he brought them back home to show off. Not saying that can account for billions, but thats just one cat who had everything against him and also was well fed at home.
Allow me to contribute another experience. At various times, I've lived alongside twelve different pet cats, owned by family members who were also avid birdwatchers; usually, the garden would be crowded with birds at the feeders.
In terms of individuals among the cats, I guess about half have tried to stalk and catch the birds, and of those probably about half were effective. But in terms of impact, that seemingly small quarter punched above their weight to be a total menace. Carcasses of the birds and other animals (even rabbits!) would keep showing up until they were stopped with a bell collar. If left to their own devices, I don't have trouble imagining they'd put a huge dent in the local ecosystem.
Incidentally, here's a critical take of a study on the amount of wildlife cats kill that made headlines in 2013 cited in the article, also by NPR: https://www.npr.org/sections/13.7/2013/02/03/170851048/do-we...