The reason for this is that SDs shipping centers doesnt include a receipt with values in the package, and there is no customs declaration on the packages to let the customs know what it is and what the value is..
I noticed this on my box when it arrived last week, it took 5 weeks from i ordered till it arrived at customs and another week of delay due to me having to sort out the paperwork.
As for your question, i would contact the customs explaining that this is a competition prize and that you dont have an invoice for it.
They will likely still require some kind of paperwork describing the value of the item/shipping aswell as what it is tho, i guess you could either:
A: Get the receipt email from someone who ordered the game and subtly edit it with the correct dates and your name
B: See if SD could make you a faux receipt for the customs..
Im sorry i couldnt be of more help 