I have ordered a lot of things from there and have never signed for one of them..so I don't think signing for them is a big factor here.

Obviously it is there fault and they made you wait all that time..so I would say, keep both of them, wait a while and if you hear nothing from them, then give it to someone as a pressie. Its always best to be safe incase they get funny about it, but I can't see that happening...they are a massive company and losing one item isn't going to worry them especially as they made you wait all that time in the beginning