It’s a bit blurred because of its single-party nature, but it has all of the attributes of a republic.
For all intents and purposes it is republic. After all republic is quite meaningless term, specially when we consider some constitutional monarchies or dictatorial leaders that don't have hereditary power.
It's a fuzzy term. As usual, not everything falls nicely in neat little boxes.
In constitutional monarchies, the monarch is still associated with "the crown" and is personally an integral part of the State, and it is almost always hereditary. Sweden and the UK are unarguably monarchies with some democratic legitimacy. I was going to write "always", but actually I'd be curious to know if there is an example of non-hereditary constitutional monarchy nowadays.
I would think that non-hereditary dictatorships tend to be republics, even if the parliament plays a purely nominal role (Azerbaijan, Russia, several African republics, etc), or just military dictatorship, doing away with any pretence and not bothering with a parliament and rigged elections (lots of them have been around; these days Myanmar is a good example). North Korea is also interesting, being a hereditary republican dictatorship.