What is the status of ruling by what Allah has revealed in Islam, and is the ruler who does not rule by what Allah has revealed considered a disbeliever?

Ruling by what Allah has revealed is part of Tawhid al-Rububiyyah (Oneness of Lordship). Whoever does not rule by what Allah has revealed desires to seek judgment from other than Allah and His Messenger. Therefore, either faith is negated from him, as in Surah An-Nisa, where Allah describes those who claim faith yet desire to seek judgment from Taghut (false deities/tyrants) and turn away when invited to the judgment of Allah and His Messenger. Allah swore that they do not believe until they make the Messenger the judge in their disputes, find no hesitation in their hearts concerning his judgment, and submit in full submission.

Or he is described as a disbeliever, an oppressor, and a transgressor, as in Surah Al-Ma'idah. These three descriptions (disbeliever, oppressor, transgressor) apply to a person according to his intention and motives: - Whoever does not rule by what Allah has revealed out of disdain or contempt, or believing that something else is better, is a disbeliever, a disbelief that expels one from the fold of Islam. - Whoever does not rule by what Allah has revealed out of tyranny or revenge is an oppressor, not a disbeliever. - Whoever does not rule by what Allah has revealed out of favoritism or for a bribe is a transgressor, not a disbeliever.

Shaykh al-Islam Ibn Taymiyyah clarified that following rabbis and monks in altering the religion of Allah, while knowing it, is disbelief and polytheism. As for obeying them in disobeying Allah, while believing it to be a sin, this falls under the ruling of those who commit sins.