Matthew,
So the quick fix is to edit the config.json where it has things like:
"config": "/webappbuilder/apps/12/widgets/Draw/config_Draw.json"
it should be:
"config": "widgets/Draw/config_Draw.json"
So just remove "/webappbuilder/apps/12/"
Now why it was set that way when you deployed the app I don't know.
Once I made those changes to the config.json I go the widgets in your app to work.