Someone not accepting the GA?

Just have patience and wait. I've had this too, maybe they are online, but on their phones or on a computer where Steam is not installed

Also:

The winner has not redeemed my gift, and I'm unable to get into contact with them. How do I proceed?

If you've been unable to reach the winner of your giveaway using e-mail and Steam after seven days of your giveaway ending, and they have not yet activated or redeemed any keys or gifts you attempted to send, please contact support to request a new winner. When creating a ticket, we ask you to include data that suggests you made an adequate attempt to contact the winner, such as screenshots of e-mails, friend requests, or gifts pending on Steam. If the request is approved, a new winner will be generated by the site.

Was the winner online on Steam? If not, they are possible away from home and can not access their Steam.
Even if you dislike it, try to add them on Steam or send them an e-mail.
Edit: Comment in an old GA of the winner, if they every given away something you can access.

Check for non-activated wins on the winner, they may be stealing keys to sell them.
If you find such history, you can provide screenshots that you sent the key and ask for forced mark received.
If not, then winner doesn't want the game (why enter for it then is a mystery), so just ask for reroll.

You should wait the full 7 days before getting too worried about it. A winner has 7 days to activate and mark a win (same as the creator has 7 to deliver it).
He/she might not be able to activate or accept the gift right now (they may be on mobile) and are online checking the forums or something.

You can contact them on an old giveaway of theirs, or a comment on Steam (if possible) if you feel the need to do so.

just saying... did the winner have access to the key yet? (did you put the key in the giveaway page or sent it via email?)

because if he could grab it, a reroll after 7 days will be risky since he could have activated it...

E-mail and contact the winner on Steam.
Take screenshots of both attempts.
After 7 days, put in a reroll request and link the screenshots within it, and ask staff to force Feedback or reroll, as needed.

Unless I'm mistaken, the winner in question only has one non-activation, and it's over a year ago for an absolutely terrible game by an absolutely terrible dev. Given that he's won and activated significantly more valuable games, and given the dev in question, It seems likely that he asked Steam to remove the game from his account without realizing that it would give his account a black mark here.

Based on his otherwise clean account, I wouldn't worry too much about it. Like others have said, give him his week and it'll probably take care of itself.

EDIT: Wait, I forgot, I can't use the word "absolute" because it's not fair. By issuing this retraction, I understand that I will be sued in the state of Arizona.