Accurate prediction of Remaining Useful Life (RUL) is critical for effective prognostics and health management (PHM) in industrial systems. However, existing data-driven methods often require large amounts of high-quality data and lack interpretability, limiting their applicability in real-world scenarios. In practice, widely used synthetic benchmark datasets such as CMAPSS and N-CMAPSS are themselves noisy due to sensor drift and mode switching, and limited in the number of available run-to-failure trajectories. In this study, we propose ST-KDFormer (Spatio-Temporal Koopman Dual-branch Transformer), a novel architecture that integrates Koopman operator theory with deep learning to address these challenges. ST-KDFormer employs separate Koopman Autoencoders (KAEs) to learn linearized latent representations of temporal and spatial system dynamics. These embeddings are jointly processed through a dual-branch Transformer encoder to capture contextual dependencies within and across temporal windows and sensor dimensions. To enable efficient end-to-end training, we introduce a unified loss function with adaptive weighting to balance embedding and RUL prediction objectives. We evaluate our approach on the CMAPSS and N-CMAPSS benchmark datasets through extensive experiments, including ablation studies and comparisons with state-of-the-art methods. The results demonstrate that ST-KDFormer achieves superior performance in terms of prediction accuracy and robustness across varying operational conditions, validating its effectiveness for practical RUL estimation tasks.