Is it permissible to conduct a race where the prize is a non-material penalty agreed upon by both parties, such as the winner hitting the loser five times, and is this considered gambling?

It is impermissible to race or wager for financial compensation or benefit, except in horse racing, camel racing, archery, and competitions that aid material or moral jihad, such as contests in Quran, Hadith (definition), and Fiqh. It has been authentically reported from the Prophet, peace and blessings be upon him, that he said: "There is no prize except in archery, or hoofed animals, or camels." If the competition is in Islamic knowledge or horsemanship, it is permissible to set a prize for the winner, even if taken from the loser. There is no harm in the benefit being a known service, such as cleaning the house. As for making the prize the striking of the losing party, this is blameworthy amusement. If the competition falls outside what has been mentioned, it is impermissible to set a prize for it.