Non-Amazon books cannot utilize the X-Ray feature, but only because the X-Ray comes from a file on the device called {book-filename}.sdr/XRAY.entities.{ASIN}.asc (and must be formatted to reference the correct locations within the book). Only Amazon officially knows how to generate them.
BUT unofficially you can duplicate much of the functionality of it using the online X-ray generator here:
http://www.xunwang.me/xray/
You will need to break open the book with mobi2mobi or Java Mobi Metadata Editor to get access to some Exth fields that must be filled out, and it can't link to the locations within the books, though it will list the Characters/themes/etc. and a Wikipedia summary, they just all link to the front of the book.
Detailed instructions are on the site.
Likewise, page numbers are at {book-filename}.sdr/{book-filename}.apnx and can be unofficially generated by calibre, but the actual page numbers are calculated via guesswork, because calibre doesn't actually know where the real page numbers go.
Other than that, the Kindle supports anything for sideloaded books as Amazon purchases. It's just difficult to duplicate these undocumented addons to the book.
I get the impression about Kobo's Beyond the Book that it works natively for sideloaded books too, by analyzing the book text for keywords.