This software looks looks like that the original version 1 software used to be available direct through the publisher OR the app store, but the version 2 release is only available through the publisher. Additionally, even the original version appears to no longer be in the App Store.
Per their website, you should follow the instructions at the very, very bottom of this web page:
https://www.yummysoftware.com/news/
You will need to contact them directly from the sound of it:
https://www.yummysoftware.com/support/contact/
Perhaps you can offer to send them a screen shot of the old discontinued App Store version in your purchase history to prove you had purchased it if you no longer have it installed and cannot follow their instructions.