Responsible gaming (RG) promotes safe gambling practices and is essential for the sustainable development of the gaming industry. Current RG systems typically utilize setting gaming limits and maintaining blocking lists. Static and rigid gaming limits can adversely affect both customer experience and operator business development due to their inflexibility. While machine learning could enable tailor-made limits, it requires exchanging sensitive data among multiple parties, such as casino operators, financial institutions, and third parties, raising data privacy and confidentiality concerns due to the sensitive nature of personal and financial information. This work proposes a pioneering privacy-preserving federated learning framework for response gaming systems to address these challenges. During model training, our approach leverages federated learning to mitigate sensitive data exchange issues. Additionally, we incorporate Labeled Private Set Intersection (LPSI) to enhance privacy protection during gradient exchanges in federated learning. Extensive experiments demonstrate that our approach is both effective and privacy-preserving.