The story in *Sonic Adventure Battle 2* focuses on Sonic and friends stopping Eggman from causing chaos, but it's a different story than the original *Sonic Adventure*.
In the original *Sonic Adventure*, Chaos is defeated and essentially "dies" after Sonic utilizes the power of the Master Emerald to seal it away. However, this event isn't directly depicted or referenced in *Sonic Adventure Battle 2*.
*Sonic Adventure Battle 2* is more of a collection of minigames and challenges based on the *Sonic Adventure* series, so there's no overarching story that would feature Chaos's demise.