They really do believe they will establish a world wide caliphate.
From Schmoozing with Terrorists.
A deputy commander of Fatah's al Aqsa Martyrs Bridade, Nasser Abu Azziz, explained to Klein that when sharia law is imposed in Western countries, "these sick people [homosexuals] will be treated in a very tough way," explaining that the Islamic leadership will "prevent social and physical diseases like homosexuality." All the terrorists whom Klein interviewed agreed that homosexuality would not be tolerated in the US once Islam rules.
And homosexuality is not all they condemn. The failure of western women to conform to Islamic standards of dress will reap harsh responses including, if necessary, torture. Sheik Hamad, a Hamas cleric, said those women who refuse to cover themselves in conformity with Islamic values would be punished either by imprisonment, whipping or stoning.