Lambik: How do you win a game of this Superchess?

The Immobilizer sounds just like this Wizard you've described. In Ultima the Immobilizer, in fact all the pieces except the King and Pawns, move as a Queen moves in regular Chess. The difference is how they capture. In regular Chess the pieces all move differently but all capture in the same manner. They capture by occupying the square held by the opponent's piece. I've heard this called, "Displacement". In Ultima, the pieces all move the same, but capture in different methods. The Immobilizer can't even capture at all. I will argue that it is a stronger piece than the chess Queen though. This Joker you've described is similiar to a Chameleon in Ultima. The Chameleon captures the piece that it is capturing in the manner that that piece captures! Longleapers are like the flying Kings I've seen in some of the Checker variants played on this site. The Coordinator is unique and can be hard to stop. He only guards two squares at a time, but threatens plenty just sitting around. The Withdrawer is a weak piece. After seeing how an Amazon works, I wouldn't mind trying Ultima with an Amazon in the place of the Withdrawer. The Pawns in Ultima move like Rooks. The capture by trapping an enemy piece between themselves and a friendly piece or Pawn.
There's no promotion in Ultima. A stalemate is a victory for the side that moved last. Checkmate is still what the object is. The King is the same as in regular Chess. You may also suicide your own piece if it's immobilized. This counts as a turn.