Is the giver of zakat absolved if he intended to count a sum from his debt as zakat, and asked the debtor to give it to another person, but the debtor gave it to that other person as a gift from himself, knowing that this person is not poor but is in need of the money?

If you intended zakat (definition) with this amount and appointed someone to deliver it to its rightful recipient, but he misunderstood your intention and delivered it to someone he thought was deserving, then if it was given to a rightful recipient of zakat, it is sufficient for you. Otherwise, it is not sufficient, and you must pay it again. The person's need for clothes is considered: if he has enough clothes and desires more, he is not eligible for zakat. But if he is in need of basic clothing and cannot afford to buy it, then he is eligible.