Winner marked gift 'not received' and I can't contact him.

Contact support.

Contact support also include screenshot that you actualy sent him gift.

You can see your gift history on steam inventory > click more > View Gift History

When he marked it as not received, while avoiding contact with you, what would want to wait for? Just contact support.

He probably doesn't check his mail and doesn't know how this site works. He probably just waited for a key to appear in the "won section".
I had a handful of users that were like that, though I was able to contact them eventually. (but in those cases I could write below one of their giveaways)

You can't really do much about it. I guess the game is still in your steam inventory? Just make a screenshot that you've tried to send it then cancel the send-progress and ask support for a re-roll and provide the screenshot to them.

Hopefully the next winner is more suitable.

I've created a support ticket with a screenshot.

@sappyMA The giveaway you commented on was not the one I meant, and I already created a support ticket to remove that giveaway.

READ FAQ ^__^

Welcome to my world. =/ I feel sorry for you.
Make a request received feedback ticket and show screenshots of the key you sent (blur out one-third of it) and how you tried to attempt to make contact. Support will try to speak to the person. if they still won't respond, you'll likely get your activated mark. It's not a 100% sure thing though.