All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, it is important to explicate the concept of Khilaafah (Islamic Caliphate) before judging whether or not a state may be described as a state of Khilaafah. The basis of the concept of Khilaafah is that the ruler succeeds the Prophet, sallallaahu ‘alayhi wa sallam, in managing the affairs of his Ummah in terms of guarding their religious and worldly affairs.
Al-Mawsoo‘ah Al-Fiqhiyyah defines Khilaafah as follows: "Linguistically, the [Arabic] term Khilaafah is a verbal noun of the verb Khalafa (past), Yakhluf (present), denoting succeeding someone or taking his place. Any person who succeeds another and takes his position is called Khaleefah, i.e. successor or vicegerent, and this is why the person who succeeds the Prophet, sallallaahu ‘alayhi wa sallam, in implementing the Sharee‘ah rulings and governing the religious and worldly affairs of Muslims is called Khaleefah (Caliph), and the office is called Khilaafah (caliphate) or Imaamah (imamate). In Islamic terminology, the term Khilaafah is synonymous with the term Imaamah, and it was defined by Ibn Khaldoon as follows: ‘The administration of people’s affairs in accordance with the Sharee‘ah with regard to their religious and mundane affairs since Allah, The Exalted, refers everything mundane to the interests of the Hereafter.’ He further explained the definition by saying, ‘In reality, a Caliph is the vicegerent of the Law Maker (i.e. Allah) in the safeguarding of the religious and mundane affairs.'" [End of quote]
It is not a condition for the Caliph to be infallible and free of faults and deficiencies, and his reprehensible qualities (or actions) do not warrant stripping him of the title ‘Caliph’. It was narrated on the authority of Abu Hurayrah that the Messenger of Allah, sallallaahu ‘alayhi wa sallam, said: "There will come after me Caliphs who shall act upon their knowledge and comply with the (Sharee‘ah) commands, and there will come after them Caliphs who shall not act upon their knowledge nor comply with the (Sharee‘ah) commands. The one who dislikes (their sinful acts) is absolved of blame, the one who disapproves (of their sinful acts) is (also) safe (so far as incurring the Divine wrath is concerned), but the one who approves and follows them (is sinful and doomed)." [End of quote, Saheeh Ibn Hibbaan (1541)] The point of the citation is that the Prophet, sallallaahu ‘alayhi wa sallam, still referred to the second category of rulers succeeding him as ‘Caliphs’ despite the disapproval of their sinful acts.
That said, the Ottoman Empire was a Caliphate, and its rulers were Caliphs, especially in its early years. It was run in accordance with the Law of Allah, The Almighty, and was a strong fortress defending Muslims and the lands of Islam against the assaults of the disbelievers. Dr. Muhammad As-Sallaabi said in his book Ad-Dawlah Al-‘Uthmaaniyyah: ‘Awaamil An-Nuhoodh wa Asbaab As-Suqoot: “In its early years, the Ottoman Empire adhered to the Law of Allah in its totality, followed the methodology of Ahlus-Sunnah Wal-Jamaa‘ah in Da‘wah and Jihaad, fulfilled the requirements of empowerment, and utilized its means as delineated in the Quran and the Sunnah. However, towards the end of its reign, it deviated from fulfilling the requirements of empowerment and moved away from its material and moral means.” [End of quote]
He also said: “The reasons for the fall of the Ottoman Empire were many, and they all revolved around its deviation from referring judgments to the Law of Allah, The Almighty, and this incurred a life of misery and distress on Muslim individuals and the whole Ummah. The adverse effects of moving away from the Sharee‘ah are reflected in the religious, social, political, and economic aspects of people’s lives. Fitnah (trial and affliction) continues to befall people until it permeates all facets of their lives. Allah, The Exalted, Says (what means): {So, let those beware who dissent from the Prophet's order, lest Fitnah strikes them or a painful punishment.} [Quran 24:63]” [End of quote]
He listed among the reasons for its fall the following: the widespread manifestations of Shirk, acts of Bid‘ah (religious innovations), and myths, and added: “In the last two centuries of its reign, the Ottoman Empire was mired in numerous manifestations of Shirk, acts of Bid‘ah, and myths, and fell in a serious deviation from Tawheed Al-Uloohiyyah (maintaining Oneness of the Worship of Allah). Accordingly, it was overwhelmed by darkness and ignorance, obscuring the true essence of Islam and obliterating the light of Tawheed, and causing it to deviate from the straight path.” [End of quote]
It is neither fair nor just to say that the Ottoman Empire was not an Islamic Caliphate, just as it is neither fair nor just to describe it as a rightly-guided Caliphate throughout its reign. Rather, it is the same as other Caliphate states that were established in the history of Muslims throughout the ages, and the situation of the Muslims under the rule of the Ottoman Caliphate was generally better than their current situation, which is characterized by fragmentation, division, divergence, and domination of the enemies of Islam over them.
Allah Knows best.