So if someone doesn't have/gift the gift he put up..

You have to wait 7 days, after that you can mark the gift as "not received" and optionally report the giveaway creator.

All you can do is hope for the best, then mark as "not received" in 7 days, or when it's obvious you're not going to get the game.

In future, just be a bit smarter about the giveaways you enter. Unfortunately, there are too many fake ones around these days, and many of them are ridiculously obvious to spot. If someone has no track record, clearly doesn't have the game in their inventory, and the Steam key isn't available elsewhere (ie GMG), there's a good chance things are not going to end well...

Also, make sure you report the "gifter". Steamgifts will be a better place without them.