I'd check with your neighbors and see if you can find out who stole it. If the USPS delivery confirmation was used properly, you are screwed. Amazon won't believe that you didn't get the package (since they have proof it was delivered) and no mail carrier is going to steal a small Amazon box.
I think that you need to check with your neighbors, apartment complex or anyone you might have told that you were getting the game from Amazon. If you have any "foot traffic" by your door (in a complex) then you might as well forget about it. Its gone. On the plus side, stealing US mail is a serious offense, you might "scare" a neighbor who stole the game to give it back.
You can get US mail that does require a signature, but it is expensive to get registered mail or return receipt.
TBW