how long should i wait for a user to redeem their gift?

They have one week to redeem it. If the winner marked it as received, they should already have redeemed it though.

Try talking to him first, and report after 7 days have passed since the giveaway ended and he still doesn't have the game in library (yeah I'd do it sooner, but rules are rules).

If the game you are talking about is Dota 2, then it will not show up in the person's games list until they have played atleast one match.