I love animals , I really do. I had a dog and one day I hope to have another, so it's not that I don't understand animals are part of a family. They are.
Well, you see some people would be just as "baffled" at that as you are about presents for pets.
But yesterday was. my neighbours dogs birthday. She's put it on Facebook. The dog was given wrapped gifts. A toy and some edible treats, as far as I can see.
Shame you weren't invited - you could have found out more! 
She has a family, so not child substitutes.
We can only thank God for that! Couldn't have a woman without children finding happiness in a way that might "baffle" people 
She treats her dogs well
No need to call the RSPCA then - that's good news!
and isn't short of money so it's not as if she's saving up.
Not sure how you are privy to that, but if true I am glad she's comfortably off.
She's always celebrated the dogs' birthdays, there's more than one!
She sounds very caring treating them all equally - she could scarcely play favourites could she?!

But this must be unusual.
It's not. As can be seen from this thread.
What is the point?
If you had to imagine answering someone who asked YOU what the point of YOU having a dog is and why you see them as one of the family YOURSELF (see your OP) you may find your answer!! 
Good luck in your journey of understanding...