I want to create region-free giveaway but...

That depends on the game I believe. If the game is region locked, the winner will get a region-locked copy and may not be able to activate it. If it's not region locked, it's not region locked.

The person above me was right. It is depend on the game that you buy region locked or not. ~

If you are not from there:

China
Hong Kong + Taiwan
India
Poland
RU + CIS (Armenia, Azerbaijan, Belarus, Georgia, Kazakhstan, Kyrgyzstan, Moldova, Russia, Tajikistan, Turkmenistan, Ukraine, Uzbekistan)
SE Asia (Indonesia, Malaysia, Philippines, Singapore, Thailand, Vietnam)
South America (Argentina, Bahamas, Belize, Bolivia, Brazil, Chile, Colombia, Costa Rica, Ecuador, El Salvador, Guatemala, Guyana, Honduras, Mexico, Nicaragua, Panama, Paraguay, Peru, Suriname, Uruguay, Venezuela)
Turkey

This should be region free for sure.

It is dependent on the game and also where you live if it is region-locked. It is also relevant in which store you are buying it. With the given information it can't be said. If you sent it through Steam or per Mail should make no difference.

If you have any doubts about whether a certain game put region restrictions on steam then I would advise you to purchase it as a gift prior to making the giveaway to avoid inconvenience for everyone involved.

Sometimes people check if you have the gift you said you are going to send if it is not in your inventory they report you. So you better have it in your inventory.

Even you send a gift by email the game you send will have the region lock in it.
So only someone in that region can add it in his-her account.
Person doesn't need to live in that area constantly but has to activate in that region.
Or try to trick Steam by VPN and changing address but in the end Steam can become aware of that fraud.

When I was living in China I bought some games Hong Kong.
And they were regional games.
I couldn't activate them in China. I had to go back :)

Now I am in Turkey with my family and my dad's account has access to my library and he can't play with my region locked games but I can.

So I am sorry but I believe you can't.
And i hope my explenation was educational enough.
If you have any more questions please don't hesitate to ask.