note: This stroy format assumes that you understand HTML and JavaScript, and that you are willing to read the story format's source code to learn how it works and what features it has.
If you look at the story format's source code you will see that there is no configuration option for disabling it's usage of the web-browser's History System.
You will also see that the Story.show() function, which is called by the Passage Transition process, uses the current value of the internal atCheckpoint Boolean variable to determine if the current state (of the story variables) should be added as a new Moment to the History System or if it should replace the current state of the current Moment in History.
The current value of the internal atCheckpoint Boolean variable is influenced by calling the Story.checkpoint() function.