Short answer:

It wasn't the theology so much as the strategy.

Discussion:

Islam is unusual among world religions in having been founded by a man with a strategic vision which he personally executed (you might perhaps compare with the LDS). If you read the Quran and Hadith, you'll find that the Prophet is -- judged by volume of his reported words-- substantially occupied by military and administrative operations. Moses, who is on the hazy fringe of legend, similarly "leads his people"-- but we've no record of him or later Jewish leaders having much interest in expansion. Christianity has no imperial mission-- until Constantine converts and Christianity absorbs (or is absorbed by, depending on how you look at it) the Roman imperial mission.

Islam thus combines the explosive military engagement of a tribal people on the edge of more populous and settled civilizations, a systematic theocratic structure, and an imperial mission. You can compare with, say, the Mongols or the Jurchens who have similar military strengths, but don't have the same philosophical/religious/juridical structure to bring with them.

While we generally recoil from the notion of "great men" influencing history, Muhammad and the Caliphs who followed him were remarkably skillful-- conquerors and governors. They had a systematic idea of how to intimidate, how to assimilate. They were opportunistic in making use of existing governing structures-- adopting Persian and to a lesser extent Byzantine administration-- into a State whose not at all modest ambition was to embrace the world.

We can see a few other conquerors with such outsized ambitions-- Genghis Khan and his successors are parallels in conquest, but they don't start with anything so clear as an imperial mission. Its striking that not only is Muhammad clear and decisive in his vision, his followers are too. What would Islam be without Abu Bakr's ferocity in the Ridda Wars? The Rebels position was that they were followers of Muhammad, but with him dead, they owed his successors nothing. Abu Bakr's victory turns one man's prophetic cause into an institution that could survive beyond the founder's passing. Similarly-- Umar, who following Abu Bakr's death divides the conquests into provinces and appoints governors (Wali); there's nothing that was predestined in that-- history witnesses conquest accomplished by a band of hungry men, who then can't govern it for more than a few years.

The spark of Islam is the conception of a structure that seems to have been present from the first, and remarkably ambitious leadership which, having won, knew what to do with their winnings.

Sources:

Hoyland, Robert G. In God's Path: The Arab Conquests and the Creation of an Islamic Empire. Oxford University Press:2014

Donner, Fred M. The Early Islamic Conquests. Princeton University Press:2014