There are several issues with your code. But it’s hard to tell when the code is not indented. Paste your code inside triple-backquotes in the forum’s editor.
The major one might be that you are simply modifying the data.group property without calling GraphLinksModel.setGroupKeyForNodeData or Model.setDataProperty (which in this case would call setGroupKeyForNodeData for you).
Another thing I notice is that you are binding the Shape.key property – yet there is no such property defined, and making it a TwoWay binding seems pointless. I highly recommend using the go-debug.js library and watching the console log output for warnings and errors.