Will it be correct if I tell them Mutah is essentially a contract between two people and will establish a marital bond with each other and that it has certain requirements which are establishing the time period, dowry, and recitation of Arabic formula?
You have mentioned the essential requirements, and reciting it in Arabic formula is not a must. As long as the due purport is said, in whatever language.
Of course, something that was not mentioned is the female being from Ahlul Kitab, her having consent from father if virgin, and other details mentioned in practical book of laws.
Furthermore, the female is the one who initiates the contract, and the male is to accept.
And Allah knows best.