While that paper singles out cats, any introduced mammal species (rats, foxes, dogs etc.) on an island with ground-nesting and/or flightless birds is a huge problem...
Yes, that's a massive issue in New Zealand. We have a programme called Predator Free 2050 aiming to address it. There are some very interesting organisations working on solutions, such as the Cacophony Project (https://cacophony.org.nz/)
Not just mammals. Fireants got most of the quail when they arrived in the woods I grew up in. Neighbors lost most of their guinea hens too. And rabbits got pretty scarce.