As the story mentions, the Japanese understood they were defeated by at least May 1945. Primarily they wanted to try and keep the emperor/royal family in place and thus they wouldn't give in to demands for an unconditional surrender as the US and UK were adamantly demanding. Had the Allies relented on that they might've been able to negotiate peace without using the Bomb.

However, as I said in another similar thread the USSR was stringing Japan along in regards to more lenient terms of surrender so that they could extract further territorial concessions from Japan's inevitable defeat. Had the war continued long enough for the Soviets to get seriously involved in rolling Japan back it would've changed the political geography of East Asia quite a bit.

Fundamentally the atomic bomb was not the only option for ending the war with Japan. It did however give a clear chance to those in Japan who did want to simply surrender to do so rather than fighting to the last man and having the country dismembered.