Human definitions are arbitrary. The dingo is considered a threat to livestock and it is controlled for that reason. Of course sheep are also non-native, but it is not being eliminated because of economic reasons.

They may have been introduced from domestic dogs, thousands of years ago, but they have evolved into wild animals that play a key role in Australia's ecosystem. There are no more large marsupial predators in Australia and without some predator, kangaroos would overpopulate. They also show characteristics of wild canids, long legs, long muzzles, molars designed to rip flesh and the alpha only have erect tails. Characteristics found in wolves, but not in domestic dogs.