I think there could be some debate about how intelligent dogs are, but let’s brush right past that and assume they’re about as intelligent as humans.

Do you innately know it’s your birthday? Without a calendar, would you be able to tell it’s the annual anniversary of your birth? Let’s imagine further still that a bunch of other creatures (that you trust, but with whom you cannot effectively communicate) suddenly approach you in celebration and give you food, objects and attention. Would you be able to figure out why?

I think if you think it’s important that your dog understands it’s his birthday and you’re celebrating it with him, then, sure, he does. Buuuuut I dunno how realistic an assumption that is.