I read an article that touches on this cultural shift and it really helped me frame the question of identity in games
https://opgram.com/how-a-foreign-game-became-more-indian-than-india/. From my own experience, Rummy has been adapted and localized in ways that make it feel familiar and culturally relevant — people have added rules, variations, and styles of play that resonate with Indian players. While the game may not be Indian in origin, its widespread integration into social gatherings, festivals, and family traditions has made it feel like a natural part of the culture.