You can give away anything that is on the list of games when you create the giveaway. If it's not on the list you can't create a giveaway for it. When large numbers of keys are given away for a game like happened with the base Defense Grid game, they get marked by Steamgifts as Free Games and removed from the giveaway list. You should contact support about this giveaway and ask for it to be cancelled so you don't get a "not received" mark against you.

freebies are games which are given say via indiegala, gleam, the massive giveaways which tend to be in the thousands wise numbers, which these giveaways dont include the ones done on steamgifts.
those mass ones dont hit the freebie list afterwards.
as most freebies usually are, enter your email to claim the key sorta thing.

there are rules against giving away games you won via steamgifts, as thats regiveawaying.

if you have extra games on steam be it gift or key wise and its listed on steamgifts your able to do a giveaway for it.
if it doesnt appear chance it was once a freebie, which i think some websites will tell you if its been free before or not.
possible isthereanydeal.com might im unsure.

the reason as to why they dont allow the whole freebies to be used as giveaways, as people would enmass abuse those giveaways as some have done before.
as they would claim 100s of keys then do giveaways for them just to boost themselfs, which would lead to people who go thru the proper method not getting a key.

https://www.steamgifts.com/about/faq this page will help ya alot on the rules and everything <3

but if you wanna run a giveaway which your unable too on steamgifts, you can make one say via the games forum on steam.
which is pretty easy like have everyone comment, then use random.org to pick a number, using that number find the comment of the same number and bam winner.
though steamgifts is better as it keeps out cheats and alts usually.

welcome to steamgifts ^w^ hope you enjoy your stay