This article was as much about human population growth, however unstated, as it was about cheetah population decline.
If you want to see animal populations growing, look at rats, roaches, cows, and others that benefit from our lifestyles.
If you want cheetahs and other animals not to go extinct, recognize that our growth models fundamentally conflict with them. The carrying capacity of the earth for humans is higher without cheetahs than with them.