Bad news, people. Euro Gamer updated their original story on the adapter's capabilities.
UPDATE 8/10/14 11.55am: The Wii U GameCube controller adapter will only be compatible with Super Smash Bros., Nintendo has now said.
The company has changed the listing on the accessory's official product page and apologised for the mix-up.
"The GameCube Controller Adapter for Wii U is compatible with Wii U and Super Smash Bros. for Wii U specifically - it is not compatible with any other Wii U software," a Nintendo UK spokesperson has told Eurogamer.
"The adapter is also not compatible with Wii and we apologise for any confusion."
Initially, the adapter's listing stated that it would be compatible with all games that utilised the Wii Classic Controller and Classic Pro Controller, as well as the Wii U Pro Controller. Both of these statements have now been removed.
I am one sad Shiryu right now. ='(