Religious extremists are pressed by their beliefs. Almost all religious extremist view the world this way, hence why they act with violence and courage.
Thus, they see the world by believers and nonbelievers, and by belief and disbelief.
In this instance, Radical Islamics believe in one true God, Allah. And they feel that if you do not believe in Allah and you do not worship Allah as they do-That you are a non-believer and that you are doing wrong by their God, and they must do right by their God by living strictly and pleasing Allah.