To be fair to the store, their privacy policy was likely designed to stop things like abusive spouses/parents tracking down people who they gave permission to use a card.
To be unfair to the store, they are probably just being stupid.
Not giving the shipping address to the “customer” is just dumb. I think it’s good to protect people from abusive spouses and parents, but if someone is using their credit card and impersonating them then that’s not quite right.
I also think it’s more likely to have identity theft than to have a spouse trying to find the new address where a mattress was sent.
My theory is that the store was trying to protect their sale and was gambling that with less info the real person would not be able to cancel the order. So short sightedness.