With the Have P.P., the relevance of the state (whether or not the shop has indeed already closed) extends to the time of speaking.
This is why in the very usual event of us hoping to still be able to purchase something, I normally use the Have P.P. - "Has it closed?"
On the other hand, I'd use the Past Simple for things that are less recent or "don't affect me so much now." Perhaps if I were the owner of several shops, and some trusted people regularly just reported to me. Way past closing hour, I could ask my staff: "Did the shop close?"
I learned these from a British grammar book, but there's also a difference between American and British English here.