Game UI development is essential to the game industry. However, the traditional workflow requires substantial manual effort to integrate pairwise UI and UX designs into a cohesive game user interface (GameUI). The inconsistency between the aesthetic UI design and the functional UX design typically results in mismatches and inefficiencies. To address the issue, we present an automatic system, AutoGameUI, for efficiently and accurately constructing GameUI. The system centers on a two-stage multimodal learning pipeline to obtain the optimal correspondences between UI and UX designs. The first stage learns the comprehensive representations of UI and UX designs from multimodal perspectives. The second stage incorporates grouped cross-attention modules with constrained integer programming to estimate the optimal correspondences through top-down hierarchical matching. The optimal correspondences enable the automatic GameUI construction. We create the GAMEUI dataset, comprising pairwise UI and UX designs from real-world games, to train and validate the proposed method. Besides, an interactive web tool is implemented to ensure high-fidelity effects and facilitate human-in-the-loop construction. Extensive experiments on the GAMEUI and RICO datasets demonstrate the effectiveness of our system in maintaining consistency between the constructed GameUI and the original designs. When deployed in the workflow of several mobile games, AutoGameUI achieves a 3$\times$ improvement in time efficiency, conveying significant practical value for game UI development.