Adding a response for future people like me
I've got a Sony PRS-T2, accessed on the laptop with Adobe Reader for PC.
I've found that adding or deleting books to the ereader using the computer's File Explorer (as suggested by a previous commenter) does NOT work.
To add books, you have to use the related program (Reader for PC) to import books onto the device.
to my understanding, personal documents aren't readable in the cloud app for the Kindle but only the kindle e-book reader.
Purchased content can be accessed through the app.
Almost all purchased content can be accessed directly through the kindle reader.