The spaceship, and in fact the whole story, come from The Bamboo Cutter and the Moon Child, a classical Japanese fairy tale, about an elderly bamboo cutter and his wife who pray for a child, and one day, while cutting bamboo, find a perfect baby girl within the hollow stem. They take her in and raise her as their own beloved daughter, and she grows to be a great beauty, so lovely that she is hidden behind screens like a princess. The bamboo cutter's family becomes wealthy, because whenever they cut a stalk of bamboo, after taking in the child, they find a gold coin.

The daughter's great beauty draws many suitors, and she sets them several impossible tasks. The stories of the princes quests, or deceptions in some cases, in attempting to fulfill the quests, takes up much of the story.

At the end of the story, the daughter tearfully reveals that she is in fact a Moon Princess, and had been banished to Earth for some sin in the Celestial Plain, but now her Heavenly Family are calling her to return. A palanquin with a royal procession of bearers come down from the full moon, and bear the Princess back into the sky. As she goes, she bids a tearful goodbye to the bamboo cutter and his wife, calling them her parents.

Although go read the link, because that's the whole story and is much more lovely than my summary.

I think the spaceship is just Okami's playful reinterpretation of the story.

And yes, that stupid digging game is where I gave up on the Playstation.