The application of games as a therapeutic tool for cognitive training is beneficial for patients with cognitive impairments. However, effective game design for individual patient is resource-intensive. To this end, we propose an LLM-powered method, \ours, for automated and personalized therapeutic game design. Inspired by the Dungeons & Dragons, LETGAMES generates an open-world interactive narrative game. It not only generates game scenarios and challenges that target specific cognitive domains, but also employs conversational strategies to offer guidance and companionship. To validate its efficacy, we pioneer a psychology-grounded evaluation protocol LETGAMESEVAL, establishing comprehensive metrics for rehabilitative assessment. Building upon this, our experimental results from both LLM-based assessors and human expert evaluations demonstrate the significant potential of our approach, positioning LETGAMES as a promising solution to the widespread need for more accessible and tailored cognitive training tools. Our code will be open-sourced upon acceptance.