I've been looking into getting one. It says in the fine print that you have to be a registered member of Sony Rewards before you sign up for the credit card in order to qualify for the points. Are you a member of Sony Rewards?
Either way, it's worth calling the issuer (Capital One, right?) to inquire about.
Edit:
So, I called Capital One, and the representative didn't know any specific information about the card (such as the terms of the offer or $50 code).
However, on the card's website, it now says that you get 5,000 points after your first purchase. Supposedly, those 5,000 points can be used to redeem a $50 PSN code. You should check how many points you've earned.