Steam gifts is allowing me to enter giveaways for games I already have.

Have you synced your account?

They might have to ask a mod first, but yeah they can do that. It's an option for situations like that, if the winner says he won the same game in another giveaway, or if the giver sees that the winner already has the game, he can reroll the giveaway.

Also, in private giveaways only (not the public ones) the giver can set restrictions like "you must comment" or "you must not have any other games in this series" or whatever, and if the winner doesn't meet these restrictions, the giver can reroll. But the restrictions have to be stated in the description for the giveaway, you can't have a hidden or secret restriction.

Tell one giveaway creator to not send the game and reroll, accept the game from another.