Dynamic graph learning (DGL) aims to learn informative and temporally-evolving node embeddings to support downstream tasks such as link prediction. A fundamental challenge in DGL lies in effectively modeling both the temporal dynamics and structural dependencies of evolving graph topologies. Recent advances in Dynamic Graph Neural Networks (DGNNs) have obtained remarkable success by leveraging message-passing mechanisms to capture pairwise node interactions. However, these approaches often overlook more complex structural patterns, particularly neighborhood overlap, which can play a critical role in characterizing node interactions. To overcome this limitation, we introduce the Neighborhood Overlap-Aware High-Order Graph Neural Network (NO-HGNN), which is built upon two key innovations: (a) computing a correlation score based on the extent of neighborhood overlap to better capture complex node interactions; and (b) embedding this correlation directly into the message-passing process of high-order graph neural networks in the DGL. Experiments on two real-world dynamic graphs show that NO-HGNN achieves notable improvements in link prediction accuracy, outperforming several state-of-the-art approaches.