Inner experience when written out in prose or verse very often looks like literature, and may well be. The difference is that an author of inner experience writes down what he considers important spiritually, the truth as he has perceived and the communication (i.e. the piece of writing) is between him and the Divine. An example (in the West) is Carl Jung's The Seven Sermons to the Dead. In literature, it is always a communication between the author and his readers. In the former, failure in communication is not a non-issue, while the latter communication failure is fatal, though in both cases a correct reading needs to be learned.
Zen stories (koans) though are in a special position. They entail enlightenment experience, yet they are embedded in drama. To fully understand the stories, one must mentally participate in the drama. In other words, one must re-enact the inner experience of the each participants in the koan. For example in the famous koan NANQUAN KILLS A CAT (南泉斬貓), a student must put himself separately into the monks, the cat, Nanquan and his famous student monk Zhaozhou 赵州.
Where then is the inner experience of Enlightenment in a koan? The inner experience of Enlightenment, if any, lies within the reader. In this regards, those who have background in literary training, in particular with training in reading plays, will have a definite advantage. That is the reason why Zen is an enlightenment route for intellectuals.