Holographic displays represent a significant application of future human-computer interaction, with desktop-based digital light field holography already seeing widespread use. As this technology develops, exploring 3D interaction design strategies and user experience research specific to holographic displays becomes essential. Despite the rapid advancements in display technology, there are still significant gaps in compatible interaction paradigms. The mortise and tenon structure, an intangible cultural heritage of China, combines concepts from philosophy, material science, mechanics, mathematics, and aesthetics. It has unique characteristics of traditional culture and spatial organization, making it a worthwhile object for developing an experience system that combines craftsmanship, art, and culture through holographic 3D display and interaction. This paper reviews the historical development, research methodologies, and frameworks for human-computer interaction interfaces. It focuses on designing interaction interfaces within holographic environments, incorporating the Chinese cultural heritage of the mortise and tenon structures. The study constructs an interactive experience system using the Unity platform, Leap Motion for gesture recognition, and a Sony holographic display screen for visualization. The project evaluated the overall performance of this holographic display interaction platform through comparative experiments (N = 16). The results demonstrate that the platform offers a positive play experience for structural cognition. The project provides valuable user data and design process as a case study reference, contributing to the education field of the holographic interaction.