I solved the problem. Prior to calling the Draggable.create function, you reference the "this" keyword in a local variable like self.
For example
initDraggableItem_Characters() {
let self = this; // references the angular 2 "this"
Draggable.create('.itemDrag', {
edgeResistance: 1,
autoScroll: 1,
liveSnap: false,
throwProps: true,
onPress: function () {
this.activeCharacterType = self.getActiveCharacterType(this.target.id); // angular 2 function call
this.startX = this.x; // greensock's this
this.startY = this.y; // greensock's this
.......
