How to export polygon coordinates to CSV (not WKT)?

Use the plugin MMQGIS to export geometry to csv. I just try with your file, it works perfectly.

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Choose Layer > Save As... with format as CSV. Make sure 'Layer Option', 'GEOMETRY' is set to AS_WKT in the 'Save vector layer as...' window. The first column of the CSV file will now include polygon coordinates.

You can use this simple app to load a shapefile, and then export as X/Y's