Entei, Raikou, Suicune - Called the Legendary Beasts, not Dogs, therefore, accepted they aren't dogs. Additionally, based on Chinese mythology, and are based on Guardian Lions.
Vulpix and Ninetails - Foxes, not Dogs. Particularly Kitsune.
Riolu and Lucario - Jackals, such as Anubis, while part of the same family as dogs, not strictly a dog.
Absol - Based on Bai Ze of Chinese Mythology. Described as a Mountain LION, not a dog.