Hmm that's odd...https://support.steampowered.com/kb_article.php?ref=7480-WUSF-3601 it's listed on the Steam redeemable CD keys too. Just have to make sure you grab the Product Key version from the Gamestop App, and not the one from the E-mail. Though from that error code it does sound like you're entering the right key, it's just not working.
Edit-Fixed link ;-p
I won that little sweepstakes too and I'm getting the same error. I wish they just gave us the Steam key, I wanna try DS1 out on my PC. >_<