Yes, Islam is authoritarian. However, you've got the axes reversed. On the right is the authoritarian forms of government where maximum power is concentrated in increasingly few hands. Go from a rather centrist republic where a small group of representatives holds power to oligarchy where a cartel or junta rule as a committee to forms were a single person holds all the power like a monarchy, theocracy, or dictatorship. You're correct to group Islamic theocracy in with Marxism on this access because they both concentrate enormous power in the hands of very few.

However, there are other axes that can be added. Usually it's an economic axis. So you can have a democracy (each citizen gets a vote, highly dispersed authority) which is capitalist or one which is Marxist.

This is sort of Political Science 101 and worth reading up on the differences between "right" and "left" in order to understand the terms. The reason you got them backwards is that the modern "Left" cloaks itself in individual liberties and claims to support democracy while in fact creating a system of government that tricks citizens into thinking they hold power when in fact only a tiny cartel/junta/cabal actually hold the power. For example, we in the US think we get to pick the President with a popular vote. It's a total lie. Two political parties choose the candidates that may go on the ballot. They do this by having a small group of party elites vote for those candidates. You get to choose one of the two choices the parties select for you. The party primaries are rigged, and so is the general election. You think you hold power when in fact, the donors who control the parties hold the power and lie to you about that.