What is the meaning of "the nearer of the two parties to the truth will kill them (i.e., the Kharijites)" as stated in the Prophet's hadith regarding the Kharijites? Are the Kharijites disbelievers, and why was there an order to kill them like the people of 'Aad?

Imam Muslim, Ahmad, and others narrated the hadith: "My Ummah will split into two factions. A renegade group will emerge between them, and the closest of the two factions to the truth will kill them." This was interpreted to mean the emergence of the Khawarij (Haruriyyah) during the caliphate of Ali, may Allah be pleased with him, and their excommunication of him and Mu'awiyah. Ali, may Allah be pleased with him, fought them at Nahrawan. Shaykh al-Islam explained that this hadith is evidence that both warring factions (Ali and his companions, and Mu'awiyah and his companions) were on the truth, and that Ali and his companions were closer to the truth. The Khawarij were ordered to be killed due to their great mischief, such as shedding the blood of Muslims, excommunicating the masters of the Companions, and distorting the words of Allah.