Get List of Purchased Items on App Store
Unfortunately the only way to do this is if you have access to a Mac (or Virtual Machine) running OS X El Capitan (10.11). I have an iMac that can't be upgraded beyond 10.11 so I'm able to do this pretty easily. I'll explain how for anyone who might be interested enough to do this in 2019 or beyond.

The App Store in El Capitan had a "Debug" menu, (which was removed in 10.12), which you can enable by entering this command in Terminal.app:

defaults write com.apple.appstore ShowDebugMenu -bool true


Once enabled, you will find the Debug menu at the far right of the App Store menus. One of its options is: "Save page source to disk"



If you open the "Purchased" tab in the App Store app, and then select "Save page source to disk" it will save the HTML to:

~/Library/Containers/com.apple.appstore/Data/Library/Documentation/pageSource.html


(I think it was /tmp/pageSource.html in an earlier version of OS X, but I'm not sure.)

From there you can use the HTML file to produce a list, or just use the HTML file if you prefer. I have a script that transforms the pageSource.html into https://mas.luo.ma for me. 

I don't know how long Apple will support El Capitan accessing the App Store, but I believe they still support back to 10.7 / Lion, so I'm hopeful it will continue for a good long time.