Re: "Books.app on Mac can't open book from Apple Store :
I downloaded my first book from the Apple book store on a Mac mini running 10.14.6 with Books.app 1.19".
"Any thoughts on what is the problem or a solution?"
Seems there could be various possible causes, and finding the right one could lead to solution:
✽ You could try quitting the Books app, Then restart your Mac (ie: Apple menu (in top menu bar) > Restart)
Wait while your Mac restarts, then log back in, and re-open the Books app. See whhether you can double-click the book in the Library, and have it open.
(Restarting your Mac deletes temporary files, re-establishes connections, may update any recent setting changes etc., and more ... also: often restores order if something is not working as expected.
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✽ Else: Wondering if there may be a clue in Apple Support's article for MacOS 10.14 Mojave
Books app may work differently on your Mac, than on your iPad.
Read books in Books on Mac - Apple Support
Above comes from the Books User Guide for MacOS Mojave.:
Welcome to Books on Mac - Apple Support To browse the Books User Guide,
click Table of Contents at the top of the page that opens from the "Welcome" link
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✽ You may use iCloud, (or want to), to sync books between your devices,
See your books on all your devices in Books - Apple Support
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✽ You could delete and redownload the book:
How to: Redownload books and audio books - Apple Support
✽ See what to do if you can’t redownload an item or if you don’t see the item in your purchases.
If there’s an issue when you redownload apps, movies, or other content from Apple - Apple Support
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✽ If needed: you can reach out to Apple Support online, or by phone in your country or region:
Contact Apple Support - Apple Support
All the best :-)