Puyo Puyo! The Medal Edition © 2009 Sega Enterprises, Limited.
This game uses Sega's "Medalink" which is a service that allows up to 16 units or four different games to be connected, but the units must be on the same location.
Released in April 2009.
Game's picture.
Game's screenshots.
Official website: http://medalink.sega.jp/game_p_in_p.html