It is an alternative world. A unified existence, where G-d, His Torah, and His people are One. Let us explain. Not a commemoration of cosmic events that occurred on this date, but a relationship with G-d, irregardless of the gifts He sometimes bestows. This longing for the Divinity highlights the distinction between Israel and the nations, clarifying why Shmini Atzeres belongs to Klal Yisrael alone.
Many nations repent from their sins, frightened of the coming retribution.
Klal Yisrael cleanses themselves for an entirely different reason. They desire atonement, but not as an escape from punishment. It is not the reward they desire, but the relationship itself, and they strive to remove the evil barrier between man and his Creator. For this reason, Shmini Atzeres is uncorruptible. The path of the nations, though at times pointed in the right direction, has more than one purpose.