This quote will be familiar to those who have studied Classical Chinese, or to those who have played the Squaresoft RPG Chrono Trigger. In the lost city of Zeal, Doreen, one of a trio of aliens, springs this bastardization of Zhuangzi on you, using it as an oblique comment on the gnostic plotline that runs through many Squaresoft games.
The original quote, one of the most famous in Classical Chinese, is from Zhuangzi:
Am I a butterfly dreaming I am a person? Or a person dreaming I am a butterfly?
This quote is known in both the high and low culture of China, as well as being passed around the West. Although it is often quoted out of context, it is not a bad summarization of Zhuangzi's philosophy.
It just occured to me that the second part of the quote is not totally random. A bowling ball is an agent of destruction, rolling towards destruction of the pins. A plate of Sashimi is totally passive and soft, waiting to be consumed. Since the plot of the game involves something buried deep in the earth's core, ready to destroy the world, yet slumbering in passiveness, this phrase could refer to how people working towards destruction can view themselves as totally passive. A quote from Spinoza comes to mind.
By using this quote and then modifying it, a reference is being made to all the lore and stories of dreams that occur in the tradition. Or, as often is the case with Squaresoft, it could just be a well.