I would describe the Poetics not as a work on the philosophy of storytelling, but as our earliest surviving example of literary theory.
Ancient Greece had an especially vibrant literary culture, in an era when few could afford books, because of the role of Dionysia, which through open competition in public, pushed the form and content of what could be expressed in theatre, as a religious sacrament. That dynamic creative competative literary culture, was a natural fit to literary theory.
The most comparable in stature and influence, is going to be the literary theory of Confucius. See for instance Confucius and Ancient Chinese Literary- Criticism. Along with Socrates, Abraham and Buddha he is seen as a key figure in the emergence of the proposed Axial Age, where religiousity shifted from focus on spectacle and feasting of sacrifices, into philosophical and theological ethical frameworks. Note the role of the Imperial Examination, in formalising Chinese literary theory and poetry, also.
The Sanskrit Natya Shastra includes literary criticism on ancient Indian literature and Sanskrit drama (consider the Arthashastra, for another example of how crucial historical vicissitudes are to what texts we have now - or the 100+ lost works by Aristotle).
Pre-Islamic Persian literature was voluminous, but little has survived, mainly what travelled with the Parsis to India. No single text devoted to literary criticism has survived from pre-Islamic Persia. However, some essays in Pahlavi, such as 'Ayin-e name nebeshtan' (Principles of Writing Books) and "Bab-e edteda’I-ye" (Kalileh o Demneh), have been considered as literary criticism.
Literary criticism was also employed in other forms of medieval Arabic literature and Arabic poetry from the 9th century, notably by Al-Jahiz in his al-Bayan wa-'l-tabyin and al-Hayawan, and by Abdullah ibn al-Mu'tazz in his Kitab al-Badi.
Literary theory does not I think generally help writers. But instead, educates audiences, who will then support more complex and challenging works in their cultural discourse (or not). The texts that an educated person within a culture is expected to know constantly shift, now more than ever. But where the literary knowledge of 'many educated people' overlap, there is still a cultural 'canon', and that is what creators create work within and against (ie, the domain of philosophy of art and creativity), just as they acknowledged and often played against Classics of the past, changing the space of creativity, as art must seek to do. Literary theory can be a crib-sheet for those who aren't going to read and make sense of the canon, to understand perspectives of those who do.