My giveaways winner set profile to private and I can't add him

Use the email to contact him then. You don't have to randomly send the key via email. Ask him to add you on Steam.

He has a week to accept the gift. If after a week he didn't, contact support and provide snapshots proving that you have attempted to send him the gift (emailed him as well).

On the giveaway that ended 6 hours ago?

Give him some time to accept your request.

Notify him through e-mail to contact you through Steam to accept his win. If, after a week from the end of the giveaway, he still has not, file a re-roll request and include a link to a screenshot of the e-mail, because we'll ask for it if you don't.

I feel like if I sent via e-mail he might doesn't know and never tick recieve gift :(

I was thinking the same. As he isn't interested in a possible winning, as he didn't put in contact with you.
Give him more time and good luck with this!

You should contact him/her via alternative means, i.e. announcemnts on the radio, billboards or skywriting.

Like everyone else has said, you can email them. you don't need to add someone in order to send a gift, if they have the wrong info in their profile that is on them, take a screen shot of the "gift sent" message if you are worried.

If a user has set his profile on private never!! send him the gift per mail.
Mostly its private cause its a leecher and will regifting...so send him an email that
he should answer your friend request...add him on Steam, check his won games and if he activated
and than if all is okay gift it to him... and if not, make screen-shoots from his gamelist and send
to support and request for reroll.