Amazon always requires a category (Browse Node ID in Amazon terminology) for all newly created listings (i.e. the UPC/EAN that you are using to create the listing doesn't exist on Amazon).
If you are creating an 'Offer' for an existing Amazon catalog product i.e. uploading your (price, inventory, and shipping data) for an existing product being sold, then a category is not required. In this case, you are using the category that already exists for that ASIN so there is no need to set it.
Setting the Amazon Category in Single-Edit Mode
Open a product on Shopify Marketplace Connect. Scroll down and look for Category, Item Type & Product Type.
Click Change Category button.
Amazon Category Selection Dialog
Click the 
Amazon Category Selection Dialog showing leaf categories
Once you have added a category to your product, you can save and publish it to Amazon.