loop through response fields and find 'esriFieldTypeOID' instead of pulling information from response.objectIdFieldName (which is only present in a response from FeatureServer layer.

gistfile1.js

if(response.features.length && !response.error){
  //loop through fields returned by service
  for (var j = response.fields.length - 1; j >= 0, j--) {
	  //find field with type 'esriFieldTypeOID' and use its name as an attribute when converting to GeoJSON
	  if(response.fields[j].type == "esriFieldTypeOID")
		  var idKey = response.fields[j].name
	}
  for (var i = response.features.length - 1; i >= 0; i--) {
    var feature = response.features[i];
    var id = feature.attributes[idKey];
    if(!this._layers[id]){
      var geojson = Terraformer.ArcGIS.parse(feature);
      geojson.id = id;
      this.index.insert(geojson, geojson.id);
      this.addData(geojson);
    }
  }
}