Create a game platform, inside my React-native app or separately

I have to make multi level games, inside my React-native app or separately in a app , which I can seamlessly give access to 3rd party android n iOS app to access.Find in attchment - the architecture, that i guess, i need. Rest u tell me, how this middle-one can be implemented. So that, my clients can seamlessly play games, without me having need to install games on their server or give them code of my games