If you don't close the app, the screen will still time out at the normal screen timeout time. But, since the app is still running, it will still be running. One has nothing to do with the other.
If you want the screen to stay on, either set a longer screen timeout (and make the screen lock time at least as long as the timeout). If you want the app to stop, either pause it if you want to go back to it later, or pause it, then use the back button to close it.