You CAN play a story while still editing it in the editor. In MY STORIES right click on the story's title, and open in a new window. Then press the VIEW THIS STORY button like normal to bring up the game window where the story can be played.
Then in your MY STORIES window, click on the edit story link for that game. Then edit to your heart's content. In the story game window, it will update pages the next time the page is displayed. If you go to the game player window, to the page you are on in the editor and had changed something on the page, just press CTRL-F5 to refresh the page and any changes will be displayed. By using two windows in this way - an internet window with the editor open in it, and the game window, you can see how any changes affect the page, play the story, etc. Just use GO BACK in the game window to go back pages and test different paths. It's easy :)