We introduce RadGame, an AI-powered gamified platform for radiology education that targets two core skills: localizing findings and generating reports. Traditional radiology training is based on passive exposure to cases or active practice with real-time input from supervising radiologists, limiting opportunities for immediate and scalable feedback. RadGame addresses this gap by combining gamification with large-scale public datasets and automated, AI-driven feedback that provides clear, structured guidance to human learners. In RadGame Localize, players draw bounding boxes around abnormalities, which are automatically compared to radiologist-drawn annotations from public datasets, and visual explanations are generated by vision-language models for user missed findings. In RadGame Report, players compose findings given a chest X-ray, patient age and indication, and receive structured AI feedback based on radiology report generation metrics, highlighting errors and omissions compared to a radiologist's written ground truth report from public datasets, producing a final performance and style score. In a prospective evaluation, participants using RadGame achieved a 68% improvement in localization accuracy compared to 17% with traditional passive methods and a 31% improvement in report-writing accuracy compared to 4% with traditional methods after seeing the same cases. RadGame highlights the potential of AI-driven gamification to deliver scalable, feedback-rich radiology training and reimagines the application of medical AI resources in education.