Totalitarianism is a political doctrine that seeks to control all aspects of a society, its economy, its laws and government, its culture.
Islam is a complete way of life, a total civilization, not just a religion. It is also a culture and a political system of Sharia laws which establish its supremacy. There is no aspect of personal and public life that is not included in the Sharia.
Not just Muslims but all people must submit to the Sharia. The very name, Islam, means to submit, submit to Mohammed and the Koran in all things: religious, political and cultural.
Mohammed practiced totalitarianism. All people around him had to submit to his demands. After Arabia submitted, Mohammed left Arabia and began his mission to have Sharia rule the world.
Both the Koran and Mohammed command the terror of jihad on non-Muslims or Kafirs until Islam dominates. After Mohammed died, the caliphs killed all apostates and conquered all the Middle East and northern Africa.
After Islam enters a society, over time, the society becomes totally Islamic. This is totalitarianism