Is what happened considered a legitimate marriage or merely an engagement, knowing that the intention was for engagement, and does the intention for marriage materialize if the contract fulfills its conditions of designation, offer, acceptance, witnesses, and agreement on a dowry?

Intention is not a condition for the validity of marriage. If it fulfills the conditions for its validity, even if it is in jest, it is valid, due to the Prophet's (peace be upon him) saying: "There are three things which, whether done seriously or in jest, are to be taken seriously: marriage, divorce, and رجعة (taking back a divorced wife)."