Notice that the scripts start loading when an theme.loaded.jquery event is fired. But none of the scripts load because probably that event doesn’t ever fire.
I would say that it’s not your problem. You are using the officially supported way of injecting app code into clients store.
It does not work because their theme designer has tampered with the content_for_header variable, which should be output inside html head. Or maybe their code failed, but that’s a task for theme Support. BTW, it’s Shella, pretty popular on themefortest.
Or you can change the way of injecting your code by actually modifying their theme files, usually layout, which has its own drawbacks.