<p>Hand Gesture Recognition (HGR) has gained significant attention as a natural and intuitive means of human-computer interaction, driven by advances in machine learning, sensor technologies, and computational power. Among these, the Leap Motion Controller (LMC) stands out for its ability to capture precise hand motion with high spatial accuracy and multiple modalities (skeletal and depth). In this work, we demonstrate that representing these complex multimodal outputs as graph structures is not only appropriate but also a significant innovation that fully utilizes sophisticated neural network architectures. To improve accuracy and generalization in HGR tasks, we present a hierarchical transformer gated graph neural network that has been improved with an intermediate fusion technique. Our architecture has been designed to overcome several limitations of current graph-based methods, including inadequate multi-modal feature integration, insufficient temporal modeling, and limited generalization across users. Using two benchmark datasets, 2MLMD and MMHGD, we examine our approach and find consistent and substantial enhancements in performance compared to the most advanced baselines. Superior accuracy, robustness, and generalizability are demonstrated by the results, confirming the efficacy of our architecture. Ablation experiments demonstrate the significance of each component in improving recognition performance.</p>