In Kuwait, an engagement is not legally binding and does not obligate either party to proceed with marriage. This is clearly stated in Article 2 of the Personal Status Law, which specifies that an engagement, a promise to marry, the receipt of mahr, or the exchange of gifts does not create any legal obligation to actually get married.
Either party has the full right to withdraw from an engagement at any time (Article 3a). Importantly, if the couple does not withdraw but the bride goes ahead and marries someone else, that subsequent marriage is not annulled or invalidated by the prior engagement (Article 3b). This means the other marriage stands as fully legal, and you would have no grounds to have it dissolved simply because of a prior engagement.
Your legal remedies in such a situation would be limited to financial recovery — specifically, reclaiming the mahr and certain gifts depending on the circumstances of the withdrawal (Articles 4–6). Emotional distress or breach of promise is not a standalone cause of action under this law. If significant sums were transferred as mahr or gifts, it is wise to document everything carefully and, if necessary, seek legal advice promptly after the engagement breaks down.
This is general legal information, not legal advice. For advice on your specific situation, consult a lawyer licensed in Kuwait.