The Beautiful Katamari Matching Game was a flash game playable on the official Japanese Katamari website. The game consisted of a simple matching game featuring all of the Cousins playable in Beautiful Katamari along with The King of All Cosmos, The Prince, and The Queen of All Cosmos. Cousins who were new additions to Beautiful Katamari were marked as new. Once a match is found, the player can view the name and description of the character on the cards and the character is also added to a character page where these names and descriptions can be viewed. To match the King, Prince, or Queen only requires one of their cards to be found. The English version of the game has different descriptions compared the Japanese descriptions. An example of this is how in the English card for Princess says she enjoys chocolate cake, while the Japanese version states she enjoys gyoza. Upon finding all matches and completing the game, the player is rewarded with a deck of Katamari-themed playing cards that they can print and cut out. Jumbo versions of these playing cards were released around We ♥ Katamari's release. They can be viewed here.
While the game is no longer playable on the current version of the website, the web page was fully archived on the Internet Archive's Wayback Machine[1], making the game fully playable, but requires flash to play. However, due to Flash being discontinued, you need a Flash emulator to play it.