Thanks for that, Harry. I know I can always rely on you for a helpful answer.
I have now downloaded the "normal" version, and it works fine on my Windows 8 tablet. What's more, it seems to happily co-exist with the dedicated Windows 8 app. So I can use a different version for each of my Amazon accounts, and I can now also open non-Amazon books, which is mainly what I want.
It seems odd the the Windows 8 app doesn't support the ability to search within a book, but I suppose that's liveable with.
Also, I found out how to close the app in "tablet" mode (when I detach the screen from the keyboard): you have to sort of drag it downwards towards the bottom of the screen until it eventually shrinks into nothing. And, as you say, you can do Alt+F4 if you have a keyboard. How this is better than having a big red X at the top of the screen is beyond me, but that's progress.
Thanks again for your help.