Somehow I don’t think these Japanese Karuta/cards were licensed goods.
The above image is from The Batcave.
According to Wikipedia, these Karuta (originally a Portuguese word for “card”, carta) are a Japanese card game that came from the Japanese game obake karuta (monster cards) of the early 19th century. Each card features a monster from Japanese mythology and a character from the hiragana syllabary. The basic idea of any karuta game is to be able to quickly determine which card out of an array of cards is required and then to grab the card before it is grabbed by an opponent.
There are various types of cards which can be used to play karuta—even regular playing cards can be used as well as weirdo Batman cards like the above.