The answer is simple, the title "Caliphate" does not necessarily mean the occupation of the two holy cities of Mecca and Medina - there is another title for that: the "Custodian of the Two Holy Mosques" but that is for another story. The title "Caliphate", rather "Khalifa" from the Qu'ran, is rather vague in terms of the succession, appointment and authority of the Caliphate. What we do know about the Caliphate was that the title was born right after the death of Prophet Mohammad, and that the Caliphate was intended to be the religious successor of the Prophet.

The vague definition of a Caliphate would ultimately cause the rise of multiple Caliphates since death of the Prophet. The Abbasids Caliphate from 750 C.E. supported the ideal of the philosopher-king, an ethically perfect caliph who acted as the protector of religion and state. The Ottoman Caliphates took the title as a way to legitimize their rule over the Arab world as well as justify their claim to protect Ottoman Muslims under Russian rule. The Mashemites of Jordan claimed the title Caliphate because they are descendants to Hashim ibn Abd Manaf, the great-grandfather of Prophet Mohammad, which gives them a justified reason to become Caliphates. Wahhabism, however, believed the Ottoman Caliphates were a heretical nation, and its self-professed Muslim inhabitants were not actually Muslims. The house of Saud, with some influence from the Wahhabis, would not have called themselves Caliphates and they were not as religiously bound as the house of Hashem in Jordan.

Sources:

Bowering, Gerhard. "Caliph, Caliphate." The Princeton encyclopedia of Islamic political thought. Princeton: Princeton Univ. Press, 2013.

Sourdel, D., Lambton, A.K.S., Jong, F. de and Holt, P.M., “K̲h̲alīfa”, in: Encyclopaedia of Islam, Second Edition, Edited by: P. Bearman, Th. Bianquis, C.E. Bosworth, E. van Donzel, W.P. Heinrichs.