Looks like some hints are needed:
1) I would describe this game as "action-packed".
2) The teddy bear is a very small section of the screen.
3) The teddy bear is merely an effect caused by the character you control.
4) The background, I would call it "a stage", is linked to another character in the game.
5) The game is quite new... published 2004, for PS2 and PC.
6) The game is part of a series... it has a number of spin-offs, and touches almost all platforms.
7) This genre is dominated by another company, so in US it is not as famous, but people who have played it would find it excellent, its gameplay much better than that famous company's products.
8) While the game has nothing to do with music, almost everything in it are references to rock music.
9) This game has good rock music. Soundtracks are being sold.
10) The character (the owner of the teddy bear) is quite... controversial.