Played games into Giveaways

If you win a game here, that game is meant to stay on your account permanently. Once you have redeemed a game, you can't give that same copy away. If you want to give away a game you have won, you will need to purchase a new copy yourself.

You cant giveaway games from your library. Only non activated keys and gifts.

Once a game is on your account, the only way to remove it is to well, remove it fully. You don't get a key back from it or anything. There's 0 way of getting a key/gift from a game that's activated on your account.

Since you've gotten your answer, I'll just suggest some light reading for you:
FAQ Guidelines
Welcome to Steamgifts! :D