The proliferation of AI systems has brought increased attention to the process of creating Interactive Digital Narratives (IDNs). There is still no formal IDN design model, as previous efforts were focused on understanding finished artefacts. This paper addresses the theoretical gap in terms of the interactive digital narrative design process by considering the role of AI and proposing a novel IDN design model that includes the possibility of collaborative interaction between AI and designers in the context of creating IDNs, thereby facilitating the systematization of knowledge. This model is an extension of the existing SPP model introduced by Koenitz, reinterpreted through a design-driven approach. This broader perspective distinguishes the creative design process, the authoring process and the data pipeline, providing a more fine-grained understanding in contrast to a unified authoring process as described in current IDN literature.