No, they're not. They're an invasive species brought to different locations around the world via human activity. The feral cats being discussed originated in the middle east and were brought to different continents by humans. North America's native cat species do not naturally target mice.
This is like saying the argentine black and white tegu is a natural part of the food chain in Florida. Please understand that humans bringing a species to a new location doesn't suddenly convert them to part of nature.
Cougars, wolves, coyotes. eagles, snakes (venomous and constrictors), hawks, and owls are natural predators of cats. Their populations have been decimated mostly by loss of habitat (same with birds). Peronnally I'd much rather be overrun by feral cats than rats any given day.
This is like saying the argentine black and white tegu is a natural part of the food chain in Florida. Please understand that humans bringing a species to a new location doesn't suddenly convert them to part of nature.