Does Sburb have a goal or are the kids just thrown into a war between Prospit and Derse? The wiki says the black pieces and king need to win but that doesn't make much sense?

The Black Army is fated to win, which is the moment the Reckoning Starts. You need to take the Black King down to stop the Reckoning, complete your Denizen’s Choice/Kill them to release the Grist Hoard to perform the Ultimate Alchemy, perform the Frog Breeding to create the Genesis Tadpole, and defeat the Black Queen and get the Ring to shoot the Tadpole into the Battlefield and create a new Universe.