Unfortunately Product Customizer doesn't currently have a built-in way of exporting product customization data (or importing customizations).
This is a feature we have on our idea board, as we understand how helpful it would be to move customizations to another store or to bulk update a CSV of options and re-import them! If you'd like to add your vote for this feature, please let us know. We'll add your email to our voting list, and we'll also notify you if we start to build this feature.
For the time being, if you require an export of your customizations (though this can't be reimported), please open a support ticket and we'll be happy to manually pull one down for you.