Bidirectional service function chain (BSFC) consists of multiple virtual network functions (VNFs). Through VNF deployment and link mapping, BSFCs can be embedded into resource-constrained mobile edge networks to provide low-latency network function services to users participating in interactive applications such as multi-player online games. Data from these users are routed through BSFCs to the edge node where the application is located for interaction and then returned to the users through the BSFCs, thus enabling synchronization among multiple users. However, the edge nodes or links have limited computing or bandwidth resources to serve only a fraction of users simultaneously. Therefore, the embedding decisions among different users can affect each other. In this paper, we propose a novel BSFC embedding strategy for interactive applications with the goal of minimizing computing and bandwidth resources while satisfying users' latency requirements. We first model the BSFC embedding problem as an integer nonlinear programming problem. Then, by closely examining the complexity of the problem, we propose a distributed algorithm based on game theory. We theoretically analyze the properties of the proposed algorithm and show that it can obtain a solution with a worst-case performance bound. Finally, extensive experiments show that the proposed algorithm outperforms several existing algorithms.