There are a couple of things happening here.
Your PDF was exported as v1.3 so your strokes are being converted to outlines, probably because of an incorrect Flattening setting along the way.
Your Illustrator file had a few conflicting settings. Although you have set your dielines to overprint (correctly), you also set them to Multiply, which is unnecessary; and because that's a Transparency Effect it is triggering the stroke conversion to outlines when it flattens on Export.
What are your exact PDF Export settings and why v1.3?
I removed the Multiply from your dieline file and have attached it here. Because Multiply has been removed, it should work fine now. Test it and report back.
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