The drag-and-drop question type is the only way you can have a student drag an object (without getting into custom programming, Flash, etc.). Depending upon the functionality you want, it is technically possible to create a series of questions that branch. For example, if there are 4 squares I could move to, each one would take me to a different screen where that piece then appears, with a new set of moves. It would involve some complex actions, but I think it would be possible.
If you didn't need them to DRAG the piece, you'd have more options. For example, instead of dragging a piece to square B4, for example, they click on that square instead. This would be a much simpler solution, because you wouldn't be dependent on the question wizard. You could just have transparent shapes over the different squares that each have a different Go To action.
Does that help?
