Mobile-centric wireless networks offer users a diverse range of services and experiences. However, existing intelligent routing methods often struggle to make suitable routing decisions during dynamic network changes, significantly limiting transmission performance. This paper proposes a dynamic adaptive routing method based on Deep Reinforcement Learning (DAR-DRL) to effectively address these challenges. First, to accurately model network state information in complex and dynamically changing routing tasks, we introduce a link-aware graph learning model (LA-GNN) that efficiently senses network information of varying structures through a hierarchical aggregated message-passing neural network. Second, to ensure routing reliability in dynamic environments, we design a hop-by-hop routing strategy featuring a large acceptance domain and a reliability guarantee reward function. This mechanism adaptively avoids routing holes and loops across various network scenarios while enhancing the robustness of routing under dynamic conditions. Experimental results demonstrate that the proposed DAR-DRL method achieves the network routing task with shorter end-to-end delays, lower packet loss rates, and higher throughput compared to existing mainstream methods across common dynamic network scenarios, including cases with dynamic traffic variations, random link failures (small topology changes), and significant topology alterations.