Accurate perception of the marine environment through robust multi-object tracking (MOT) is essential for ensuring safe vessel navigation and effective maritime surveillance. However, the complicated maritime environment often causes camera motion and subsequent visual degradation, posing significant challenges to MOT. To address this challenge, we propose an efficient Dual-branch Maritime SORT (DMSORT) method for maritime MOT. The core of the framework is a parallel tracker with affine compensation, which incorporates an object detection and re-identification (ReID) branch, along with a dedicated branch for dynamic camera motion estimation. Specifically, a Reversible Columnar Detection Network (RCDN) is integrated into the detection module to leverage multi-level visual features for robust object detection. Furthermore, a lightweight Transformer-based appearance extractor (Li-TAE) is designed to capture global contextual information and generate robust appearance features. Another branch decouples platform-induced and target-intrinsic motion by constructing a projective transformation, applying platform-motion compensation within the Kalman filter, and thereby stabilizing true object trajectories. Finally, a clustering-optimized feature fusion module effectively combines motion and appearance cues to ensure identity consistency under noise, occlusion, and drift. Extensive evaluations on the Singapore Maritime Dataset demonstrate that DMSORT achieves state-of-the-art performance. Notably, DMSORT attains the fastest runtime among existing ReID-based MOT frameworks while maintaining high identity consistency and robustness to jitter and occlusion. Code is available at: https://github.com/BiscuitsLzy/DMSORT-An-efficient-parallel-maritime-multi-object-tracking-architecture-.