Not true, the most important element in the "cultural war" is the umma and re-establishing the caliphate.
Do you equate "caliphate" with an Islamic vanguard of pure believers as theorized by Sayyid Qutb? According to his work "Milestones" his was a more mystical vision that seems to borrow freely from Marxist theory. This vision anticipates a social order where no man is lord over any other man, but all voluntrily submit to the will of Allah and live lives governed strictly according to the Sha'ria. He insisted he was not proposing a theocracy by proxy, but it is hard to understand how worldwide implementation of the Sha'ria could happen in the absence of an authoritarian system.