I get that it's possible in some circumstances that for some people losing their dog will be harder than losing a relative, but I think for the vast majority of people and circumstances this is not going to be the case.
The article even ends with:
>While the death of a dog is horrible, dog owners have become so accustomed to the reassuring and nonjudgmental presence of their canine companions that, more often than not, they’ll eventually get a new one.
You can replace the love a dog gives you, and most people end up doing just that. You can't replace the love your father gives you. You can't replace the love your best friend has given you since you were 8. You can't replace the 50 years of life you were planning to share together.