1. First of all, it can fit a theoretical definition:

   From [B5 Wikia](http://babylon5.wikia.com/wiki/Emperor_of_the_Centauri_Republic):

   > The actual day to day business of running the republic is mostly handled by the Centaurum, which officially acts in an advisory capacity to the Emperor and the Royal Court and in theory has no power of law and **can only override the Emperor with a three quarter majority vote by its members**

   Due to the fact that a parlament in practice (even if not in theory) can override the Emperor, it somewhat fits - with some winking, nodding, and particular-point-of-view - both the political-science-theoretical definition of the Republic ("a form of government in which power resides in the people", as per Merriam-Webster).

2. Second, while "in modern times the definition of a republic is also commonly limited to a government which excludes a monarch" (from [Wikipedia][1], and you can see the evolution of the term there), etymologically, Romans themselves sometimes imbued the word with a different meaning:

     > While Bruni and Machiavelli used the term to describe the states of Northern Italy, which were not monarchies, the term *res publica* has a set of interrelated meanings in the original Latin. The term can quite literally be translated as "public matter".... **It was most often used by Roman writers to refer to the state and government, even during the period of the Roman Empire.**

3. Also, history knows both examples of:

   - monarchies that were considered Republics (e.g. [Kingdom of Axum][2], modern British Empire)

   - countries named "Republic" that were in fact monarchies, or at least had the power vested in a single ruler even if said ruler wasn't hereditary (e.g. totalitarian Stalin's USSR and Mao's PRC)

   As such, it's possible that Centauri was (mis)named in the same tradition.

  [1]: http://en.wikipedia.org/wiki/Republic#Political_philosophy
  [2]: http://en.wikipedia.org/wiki/Kingdom_of_Aksum