A dog cowed by a near-death experience courageously travels against all odds through 2000 miles of mountains and glaciers and predatory wildlife to be with the ones he loves, and the message you get is a property rights violation?
I suppose in a way that could be one of the messages: that sometimes in life emotions conflict with law, and that the lawful path isn't always the moral path. You'll find that particular message is hardly unique to this story (in fact some stories go so far as to scandalously suggest some laws themselves might not be just! I digress..) But, the kid's dad discouraged him from thinking he could keep the dog - at least until it was obvious from Kavik's escape and epic journey that he simply would not stand being separated from the family. And it's not like the family stole the dog; he ran away. Besides, the owner's offer to sell the dog to the family should have quelled any custody concerns.
there was no clear reason why the initial owner of Kavik shouldn't be able to keep a dog he rightfully owned.
With all his resources, the owner proved unable
to keep the dog. The owner clearly had no emotional connection to the dog (and the feeling was mutual); Kavik was just a trophy to him, and was miserable (to the point of escaping by leaping through a friggin' window
), and very likely would have remained so. It could be argued that it is unethical (and possibly illegal in some parts) to keep an animal in misery.
Sure if my dog seemed happy enough but got loose and some stranger in town found him I'd probably ask for the dog back, but the circumstances presented by the story, unrealistic as they may be, are entirely different.
Given the context of the story, it seems to me the decision of ownership never really was the owner's (or any of the humans' for that matter).