The review link does not work in the test emails because you have not made an actual purchase and the system doesn't have a product review link to populate in the template. The paragraph below the Amazon button that houses the link refers to the product as %amazon_product_name%. This is because there is no product to associate the email with.
If you go to any of your customers in the "customer" section and highlight their name you will see detailed customer info on the right of the screen, within this info is the product they have purchased. This information to populate a given template with specific customer purchase info is pulled from the Product Group. This is info taken from Amazon. For example, the XYZ product has a SKU of 2Y-ABCD-EFG8. It is represented in the Groups section as "Buyers of 2Y-ABCD-EFG8". If you where to go to that "Group" and click the pencil icon to edit it would display the Amazon info as it relates to that product. The review link is also there.
For someone that purchased your XYZ product and is sent an email via WaveReview the variable "%amazon_product_name%" will show as "XYZ Veggie Capsules, 100% Pure XYZ Root Powder" and the link associated with the Amazon button is also a variable, %amazon_review_link% and will lead to the proper URL, https://www.amazon.com/review/create-review?ie=xxxxxxxxxxxxxxxxxxxx
The "Test" email is more of an aesthetic test. Unless you are in the WaveReview system and associated with an actual purchase to populate the variables then the variable show in place of the product info or URL.