The Charity Gift to an Individual-What Is It?

From Tom Smith at The Right Coast:

Something you can do these days is give someone the gift of having given a gift yourself to some charity. So you might get a card that says, We have given a goat on your behalf to the village of Ubuti in East Ubutistan. As a follow on, you might get a picture of the villagers posing with their new goat, which is from you, sort of.

I'm not saying this is not a nice thing. It is a nice thing. What puzzles me is just what it is. Not from a legal point of view. I'm not aware it raises any legal issues, interesting or otherwise. I just think it's a little baffling what it is. Is it a gift? Somebody says to you, instead of giving you something you don't really want or need, I have elected to give some people something they really do want and need. But then what does that have to do with me? Supposedly, the person sort of forgoing the gift gets the credit for it, but what credit is there, really? I didn't give anybody a gift. Nobody asked me if I wanted to forgo a gift in order to enable the goat giving. I just get a card that says, you just gave a goat to someone, to which I might reasonably respond, I did? Maybe the idea is that the giver thinks I am such a good person I would prefer to have a goat given than to get a gift myself. Well, thanks! If you get a gift of this sort, do you write a thank you note for it?

A commentor noted that the donor, but the not the quasi-recipient, gets the tax break.