The first, posted in August 2013, was spotted by the SPCA, which started investigating the two men, believed to be hunters.
In it, McKee is seen restraining an adult male goat while encouraging two pit bull-type dogs to attack it. The dogs bite the goat's face, lips, nose, and neck while McKee laughs and shouts encouragement. The goat dies after McKee cuts its throat.
Three more videos were uploaded to Manukau's Facebook page showing McKee baiting a second goat.
When officers searched their homes, four videos of the incident were discovered.
In one video, McKee is seen cutting off the goat's head and throwing it to the dogs.
"This case is an example of an alarming increase in what you could call 'recreational cruelty'," Ric Odom, CEO of SPCA New Zealand, said.
"This tends to feature young men and the subjects of their cruelty are usually so-called pest species, like possums, goats, and rabbits. They often film themselves doing it and then post the videos on YouTube or Facebook. Sometimes they justify their behaviour by saying the animals are 'just pests'.
"Let's be very clear about this: New Zealand legislation is designed to protect all animals against this kind of abuse."
Bill O'Leary, national president of the New Zealand Deerstalkers Association, said hunting organisations had "worked very hard" with the Ministry for Primary Industries, the Department of Conservation and animal welfare groups to draw up a code of ethics for hunters.
"A wild animal deserves respect, and unnecessary cruelty is just unacceptable," he said.