There is nothing equivalent to kavya in the Abrahamic relogions. That is because liturgy is, for the most part, disconnected from the performing arts. There is no equivalent Jewish, christian or Islamic dance, epic or drama or performing arts, that would serve as a full fledged pathway to god and be considered on par with the Bible/Quran and prayer. In fact, western theater and literacy arts are largely of Greek and/or of Roman origin, from pre-christian era of paganism. Even in Greek tradition, theater and art did not serve the same Parmarthika purpose that they serve in Hinduism.
Indian culture whose sole aim to move one from worldly life to transcendence has now become a Nach-Gana. It has become part of tourism which used to be part of education. Rajiv Malhotra in conversation with most famous, prominent dancer Sonal Mansingh explores more about culture and it present scenario in India.