The English name for this games is Little Busters-EX: DOTABATA Ranking Battle. As with other card games published by Arclight Games, this game follows the deck building system made popular by Dominion.
The theme of this Japanese card game is based on a 2007 Japanese visual novel and manga by the same name. According to Wikipedia, the story behind the game features a group of high school friends who go by the name, "Little Busters." Characters include Kudryavka Nōmi (クド, "Kudo"), Rin Natsume, and Saya Tokido.
'Little Busters!' on Wikipedia
In similar style to the physical fights depicted in the visual novel, players of the card game battle classmates against each other armed with slapstick weapons like volleyballs, sea urchins, cats and eel pie to accumulate points to win the game.
The base game consists of 300 cards and a copy of the rules in Japanese.