http://www.chess.com/analysis-board-editor
That should do what you want, if I'm reading your request correctly. You can't really export but can copy the PGN out and save it yourself however you like.
Though, if you mean the mobile app when you say "app game" and not the website, then you can't.
I want to have some kind of 2 player mode, when I enter my moves into the app game, so I can then export the PGN (instead of writing it on paper)
Can the app support this?