Actually, as 'we' use and understand love, no, your dog doesn't.
If you want to generalize love to the point where it encompasses familiarity coupled with good feeling coupled with physical pleasure, then okay.
But, as we -- you and me -- think on love, such a generalized definition falls short of what we feel when we love.
Why?
Because when I love, when you love, we love the person for who she is. We understand her not only for the 'object' she is or the concreteness she provides, but also for the idiosyncratic 'subject' she is.
Your dog 'loves' you for 'what' you are. It can never know 'you', only what you serve as the source of.
The dog has no sense of self. No 'I'ness dominates it. Love, as complete, is the transaction between a 'you and me', not 'me and it'.
Now: you may love your dog, but your dog does not, cannot, love you in the same way. This makes for a one-way street...
