First of all, it can fit a theoretical definition:
From B5 Wikia:
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 - the modern political-science-theoretical definition of the Republic ("a form of government in which power resides in the people", as per Merriam-Webster).
Second, while "in modern times the definition of a republic is also commonly limited to a government which excludes a monarch" (from Wikipedia, 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.
Also, history knows both examples of:
monarchies that were considered Republics (e.g. Kingdom of Axum, Dutch, modern British Empire)
Please note that the British Empire comparison is VERY relevant, since J. Michael Straczynski himself saw Centauri like the British:
For a thousand years, the Centauri Republic was a force to be reckoned with. Like the English empire once upon a time, it held hundreds of planets in its control. It was a great military power. But slowly, as can happen, they grew content, and lazy, and gradually their own empire began to slip between their fingers. A world deciding to go rogue was troublesome, to be sure, but it's SO far away, and it's SUCH a bother to go take care of it, when we can easily get the same things from other places...let them go. They'll come crawling back sooner or later.
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, or North Korea. Or, for that matter, Rome while it was transitioning from Republic to Empire - and many observers noted that Centauri are VERY much patterned on Rome, even more so than on ~1900 British Empire)
As such, it's possible that Centauri was (mis)named in the same tradition.
