I would love to give games from this site to my friends for Christmas. I would love it if this site had a "Give Gift" option at checkout like Steam does. Or does it have this feature and I just can't find it?

/sign
I'm waiting for this feature too!

There are half a dozen topics on this already, use the search function.
To answer your question: no, this isn't supported yet, but is planned to be added, before Christmas if possible.