Weird cause Azahiel did participated in my giveaway and PM'd me a couple of days ago, so he is still active...
It is possible the email didn't get sent cause of various steamgifts server problems, or just never checked email.
Thanks to all of you for the advice. I'll make sure to let the full 7 days pass, and will try adding Azahiel on Steam. I sent the gift about an hour after the giveaway ended, but the gift is still in my inventory, saying "sent to _______ (winner's email)." Knowing s/he's been active recently, I'll try to make contact before requesting a re-roll. Thanks, all! :)
EDIT: All cleared up. Sorry for the worry, folks! Got in touch w/ the winner on Steam and the prize was delivered. :)