A veterinarian said the dogs inflicted significant violence on the goat, and McKee had encouraged this, prolonging the suffering and slow death of the goat, the SPCA said.
Three more videos were uploaded to Manukau's Facebook page showing McKee baiting a second goat while Manukau filmed him.
When officers searched their homes, four videos of the incident were discovered.
They show McKee dragging a goat by its right hind leg -- the animal appeared to have an open fracture in the femur -- while pit bull type dogs attack the goat.
The goat's screams can be clearly heard throughout.
Three dogs repeatedly bite the goat on the neck and face. The goat tries to flee but collapses on its fractured hind leg.
Both men could be heard enthusiastically encouraging the dogs throughout.
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. Even though the act of hunting and killing an animal is a lawful activity in New Zealand, once an animal has been 'captured' for the purpose of killing it, people are legally obliged to kill it in such a way that the animal doesn't suffer unreasonable or unnecessary pain or distress.
"The recently passed Animal Welfare Amendment Act has strengthened these obligations by creating specific offences for the reckless and wilful ill treatment of wild animals. It is simply unacceptable to encourage dogs to attack a wild animal that has been captured and we will vigorously investigate anyone who does so."
-NZH