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All detection from the camera is done on device, no camera data is sent off-device for processing. In the Pro version, the app comes with a SQLlite database for saving game history. This functionality is initiated by you, the User of the app, if you want to save game history. When saving a game to history, if player names are provided, they are persisted in the database along with the associated game data such as game type and roll data. This information can be shared from the app to other apps by user-initiated functionality.
Your camera data is not shared. You can save data about your games if you buy the Pro version. The only saved information is data about the games being played.