I'd again commend Habeck's Knowing the Enemy. It is true that the jihadists are not Leninists in terms of having a concrete alternative blueprint. But that's because they believe that the alternative has already been spelled out. For them to offer a blueprint for a better society would be arrogance since, from their perspective, God has already provided such a blueprint.

In a way, that makes them a more difficult opponent in the war of ideas. With communists, we could eventually say, "See what life under communism is like. Is that what you want?" But since the jihadists say that their model was the first few decades after Mohammed and to deprecate that era is to "insult" Islam, we are not able to legitimize it.
Note that this is pure jihadi ideology. To my mind one should not confuse jihadi political "theory" (al-Qaeda & associated radical revolutionaries), such as it is, with the more politically based model propounded by, say, the Egyptian or Jordanian Ikhwan (Muslim Brotherhood). Ikhwan writers speak of the pure days of Muhammad and his companions as example but focus on real-world provision of services, cleaning up corruption, and social conservatism when making the case on the stump.

This is the real battle of ideas - not Western democracy vs. the apocalyptic Caliphate. No Muslim nation is going to ever vote for or accept al-Qaeda as its leadership. Pure jihadi ideology is more in the nature of a recruiting pitch, aimed specifically at pulling in martyrs to wage jihad against foreign domination or oppressive rulers. It is not really aimed at transforming societies.

A real danger is missing the forest for the trees in the differentiation between radical jihadism and mere political Islamism.