Nowadays, the potential of games to promote well-being and social inclusion is already widely documented by research. Yet, how this potential can reach out to underrepresented communities, namely those with very specific accessibility needs, ensuring their participation is still somewhat unexplored. The present article discusses accessibility, participation, and inclusion as three pillars to address the relationship between gaming and Intellectual Disability (ID). Through this approach, more participatory models of game development and research are proposed, including the operationalization of the social model of disability and the relevance of the context. Therefore, it proposes concrete models, where accessibility is part of the creative process, to better include the voice of the player with ID into gameplay, and ensure a final media object that, more than accessible, narratively represents the experience of having this disability.