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.