The fabric look of the stage is based on the art style of the game which is a very realistic fabric style. The platforms are held up since they are made of fabric instead of just floating platforms. The transforming aspect comes from the stage being made of yarn so it could be unraveled and replaced.
This is the first stage based completely on an unreleased game at the time of the game's release. Yoshi's Woolly World is due mid 2015 while Super Smash Bros. for Wii U came out November 2014. Shadow Moses Island did feature elements from a future Metal Gear Solid game but the island itself was from Metal Gear Solid: The Twin Snakes.
This was the only starting stage in the game that was not revealed by name in the 50 Facts Extravagazana Nintendo Direct. It was in menu screenshots and previews by the press, but it wasn't until November 6, 2014 when actual official screenshots via Picture of the Day.