Q: I have recently deauthorised devices and reauthorised current 2 devices. I purchased some music on one pc with my account and an audio book from the same ccount on another PC. Neither downloads the purchases showing on the oter pc purchased lists.?????

Depending upon what country that you are in then you might be able to re-download music purchases on your other computer, as described on the page that you linked from (music can't be re-downloaded in all countries). You might also be able to turn on 'automatic downloads' so that any future purchases are downloaded automatically on that computer : automatic downloads.

Audiobooks (and ringtones) and currently one-time only downloads from the store - I believe that they are all supplied to Apple from audible.com, so I assume that it's them who are requiring the one-time download. To get it on your other computer you will need to copy it to it yourself e.g. via home sharing, external drive, flash drive etc : http://support.apple.com/kb/HT4527