It seems to be a known issue.
Next to "Login" on their web-site, click on "Support", and look at the known threads in their knowledge base (I prepared a direct link to it but it doesn't seem to be working for some odd reason). Perhaps wait until the 31st to see if you'll receive your key. If not, perhaps contact their support to let them know that - if anything - you did not order the Broken Steel DLC and you're simply waiting (and wanting) the Fallout 3 GOTY key instead.
Here are the emails I sent and their reply...
FIRST EMAIL:
I clicked on Fall Out 3 game of the year addition and it gaveme Fall Out:Broken Steel
I need the Game of the Year Edition for $4.99
Please contact me asap
THEIR REPLY:
Thank you very much for your ticket.
I can see you have recently purchased:
Fallout 3: Broken Steel
Fallout: New Vegas
Unfortunately we are unable to swap this title for another or offer a refund as key has already been sent to your account.
Kind regards,
Marc
Green Man Gaming & Playfire
Customer Service
MY REPLY:
This is UNACCEPTABLE...
I ordered the GAME OF THE YEAR EDITION of FALLOUT 3 and the wrong key was went to me by YOU guys!
I have not activated the key either because YOU sent me the wrong game...
Please rectify this immediately or I will contact my credit card company and have them deny payment to you...