Is a friend's promise of a gift upon success in an exam considered a vow to other than Allah?

What you issued was a promise of a gift, not a vow (nadhr), because a vow is a commitment that was not made. Therefore, you must fulfill your promise to your friend if you are able, because breaking a promise without an excuse is one of the characteristics of hypocrites. The Prophet, peace and blessings be upon him, said: "The signs of a hypocrite are three: whenever he speaks, he tells a lie; whenever he promises, he breaks his promise; and whenever he is entrusted, he betrays his trust."