My Bioshock 2 Giveaway

You don't need proof. You are fine.

"we guys" in the forum have nothing to do with your giveaways or why they were deleted, please go to https://www.steamgifts.com/support open a ticket and wait a year for an answer

You don't need to prove anything. It's all good if you send the game within 7 days after the giveaway ended.
One could also not own the game and buy it after the giveaway ended...

you dont have to prove that you actually have the gift, it is obvious when you write in the comments that it is a steam gift and will be given away to the winner through steam

if a previous one of your GA got removed, most likely that was not because you did not give any proof beforehand

You don't need to prove you have the game to make a giveaway.
Your previous giveaway probably got removed for other reasons, for example, the game was given away massively for free, it would not be allowed to be given away on this site.
If you check your previous giveaway that was removed, it should state the reason why it was removed.

Okey thank you guys, just was curious. :)