A theocracy is a state ruled by religious law and governed by the clergy, so yes, Islam is a theocratic system. The fact that it is a false religion is another matter.
Islam is a complete system that allows nothing to escape it. The religious law is the civil law, the economic law, and the social law, and ultimately, the mullahs rule. Of course, ultimately, rulership belongs to the “guardians of the holy places,” the Arabs (Mohammed’s tribe), which was exactly what Mohammed set out to do in the first place.
But if Islam is not a religion, but an ideology, they are governed by ideological laws and ideoligical “clergy”. From my viewpoint if Islam can claim it is a religion, or theocracy, then so is/was Nazisim and Marxism.
Other Arabs like those in Yemen (Shebans etc.) or the related Semitic tribes were not as backward as the Nejd bedouins.
And the modern day "Arabs" are really Berbers or Arameans or Assyrians or Copts etc. except for the Saudis and Kuwaitis and Omanis and Emiratis