is it possible for me to gift someone a game...

There you go.

we don't sell games here, we give them away for free. as "gifts." :)

Go here Here is for gifting only

site is called steamGIFTS, asks about gifting in title... then asks about selling.... What?

by selling i meant gifting :?

I'm not sure I understand your question, but I think I know what you're driving at. If the game is in your library, then it's already bound to your account and you cannot make a giveaway for it. If it is in your Steam inventory then you can make a giveaway for it. If you have an unredeemed Steam activation key, then you can make a giveaway for it. There are exceptions, so check that FAQ to see keys that are not accepted. If the game was added to your library, and you are receiving a message to enter a key in-game for some reason, as some games do, then that is not a valid key for a giveaway (I'm assuming you know that, though--I mention it for completeness, just in case). As several people already mentioned, selling and trading are not allowed here, and I assume it was an error in word choice. I hope this answers your question.

protip: edit OP and change sell to gift

I do my trading in the Steam Trading Forum