Practical studies using Table-talk Role-playing Games (TRPGs) targeting children with autism spectrum disorder (ASD) showed how these games promote conversation amongst the children. However, the role of the game master (GM) in facilitating conversation has not been examined. In this study, we quantitatively and qualitatively examined the relationship between the GM's comments during TRPG activities and the participant children's statements. Using conversation analysis methods, we examined the effectiveness of GM interventions in assisting children with ASD to proceed with conversations voluntarily and cooperatively. The results showed that the GM, as one of the participants, provided effective suggestions for the children to proceed with the game. The children noticed this and enjoyed the game as a whole, suggesting the difference in our approach from SST and other methods.