So, I did not get the exact deal, but something similar. The chat rep basically said it's not a real deal, but they gave me a $60 giftcard when I placed the order. So no extra $10 gift card, but still basically a buy one get one. They even added the tax onto the giftcard.
Here's a portion of the Chat transcript.
"Me: No, It was for a free game. According to the email, It was a buy one, get one on the game. I had a friend that had the store honor the same deal as well, with a $10 giftcard for ordering instore pick up
REP: Alright I am sorry that this is not a real promotion so what I can do is if you purchase the item in store or online I can offer you a Target Gift Card for the Free item but I can not add a $10 gift card.
REP: So that's a $60 Gift Card with a purchase as a one time courtesy.