This is a quite a complex task you are trying to achieve and there is no, one-click solution.
The hard way is to import the source .AI file into After Effects, convert it to a shape layer with "Create Shapes from Vector Layer" and if everything looks ok with the shape layer, copy every vertex coordinates of every shape in every group to your script and have your script rebuild the whole shape structure.
If I were you, I would start by building a small intermediate tool to show me all the vertices of a shape and then copy/embed these vertices inside my script.
Keep in mind that, except for the coordinates of each vertex you will also need the IN and OUT tangent values.
So, if you have a path selected in the timeline (e.g. Shape Layer > Contents > Shape > Path 1 > Path) and run the code below in Extendscript, four prompts will pop-up revealing you all the necessary info to rebuild the selected shape.
var vertex_text = "";
var inTangents_text = "";
var outTangents_text = "";
selectedPath = app.project.activeItem.selectedLayers[0].selectedProperties[0].path.value;
for (var i=0; i < selectedPath.vertices.length; i++) {
vertex_text = vertex_text + "[" + selectedPath.vertices.toString() + "]";
inTangents_text = inTangents_text + "[" + selectedPath.inTangents.toString() + "]";
outTangents_text = outTangents_text + "[" + selectedPath.outTangents.toString() + "]";
if (i < selectedPath.vertices.length-1) { vertex_text += ","; inTangents_text += ","; outTangents_text += ","; }
} // end for
prompt("The coordinates of the "+i+" vertices of the selected path are: ", vertex_text);
prompt("The inTangents of these vertices are: ", inTangents_text);
prompt("The outTangents of these vertices are: ", outTangents_text);
prompt("The selected path is: ", (selectedPath.closed?"closed":"open"));
You can read about the Shape Object and how to create shapes in Extendscript here: http://docs.aenhancers.com/other/shape/?highlight=tangent
If your shape is quite complex with merged paths etc. (like the reindeer example you mentioned) then you will have to recreate the whole group structure of the shape inside your script. The next step would be to streamline and automate the above process and start building your final script (adding groups, colors, outlines, merging paths).
It is a difficult task, but with a lot of patience it's doable.