Welcome to our forum.
I understand your issue, WIshlist plugin is designed for WooCommerce, although it will work on custom post types, i have tested for default post without activating WooCommerce and its still working fine for post to add wishlist and create new wishlist. Can you please check browser console area to check is there any js error is showing?
The features you are looking for still may not available. like custom field integration and remove from wishlist if post is deleted, hope future version will bring these features.