I think this service is not a place for manipulating with Game data. Besides in that case we have to 3 places where ListOfChanges field is set-> gameChangesManager, toastService and game view model which is confusing. I suggest to following:
1) in GameChangesManager check if we should show toast (  _navigationService.CurrentSource.OriginalString == _navigationService.UriFor<GameDetailsViewModel>) and as always broadcast gameChangedEvent
2) here in ShowGameChanged method just show toast with attached handler with navigation ( if this method is fired we already know that we are on different window
3) in GameDetailsViewModel show diff dialog and clear ListOfChanges field on view entry ( like now), but also when we get GameChangedEvent for currently displayed one