I would imagine the players who won would know first, but i doubt they will announced the winners... I say this because of this clause in the contract. (But i can only hope they announce the winners on the forums, or atleast someone who won could confirm the prizes are already given.

"10. WINNER'S LIST; RULES REQUEST

For a copy of the winners list, send a stamped, self-addressed, business size envelope after November 6, 2013 and before January 6, 2014 to Square Enix at the address listed below (Attention: Doppelganger Screenshot Contest Winners List). To obtain a copy of these rules, send a stamped, self-addressed business size envelope to Square Enix at the address listed below (Attention: Doppelganger Screenshot Contest Rules Request). "