Dynamic hand gestures play a pivotal role in assistive human-robot interaction (HRI), facilitating intuitive, non-verbal communication, particularly for individuals with mobility constraints or those operating robots remotely. Current gesture recognition methods are mostly limited to short-range interactions, reducing their utility in scenarios demanding robust assistive communication from afar. In this paper, we present DiG-Net, the first dynamic gesture recognition framework enabling robust operation at hyper-range distances of up to 30 meters, specifically designed for assistive robotics to enhance accessibility and improve quality of life. Our proposed Distance-aware Gesture Network (DiG-Net) effectively combines Depth-Conditioned Deformable Alignment (DADA) blocks with Spatio-Temporal Graph modules, enabling robust processing and classification of gesture sequences captured under challenging conditions, including significant physical attenuation, reduced resolution, and dynamic gesture variations commonly experienced in real-world assistive environments. We further introduce the Radiometric Spatio-Temporal Depth Attenuation Loss (RSTDAL), shown to enhance learning and strengthen model robustness across varying distances. Our model demonstrates significant performance improvement over state-of-the-art gesture recognition frameworks, achieving a recognition accuracy of 97.3% on a diverse dataset with challenging hyper-range gestures. By effectively interpreting gestures from considerable distances, DiG-Net significantly enhances the usability of assistive robots in home healthcare, industrial safety, and remote assistance scenarios, enabling seamless and intuitive interactions for users regardless of physical limitations.