Unfortunately, you can't buy default.
And you shouldn't.
See here a detailed description of the Gift Registry concept.
Usually a gift registry is opened for a specific event and is sent out to the people you know and know you.
So if you want to send the gift to some friend you should have his address :).
Technically you can get the addresses of the gift registry owner like this:
First get the customer id:
$customerId = $model->getCustomerId() where
$model is an instance of the gift registry.
Then get the customer:
$customer = Mage::getModel('customer/customer')->load($customerId);
Then get the addresses:
$addresses = $customer->getAddressesCollection();
You can try to merge in the shipping step the current customer addresses with the gift registry owner addresses or you can create a custom dropdown with the gift registry owner addresses and when you select one of his addresses, it will be like selecting 'New address' and you automatically fill in the fields with the address you selected.
I would go with the second option. This way the checkout process will go on just like it would if you fill in an address manually. It's less work and fewer risks.