The Library is not your Creative Cloud files directory. These are two separate things. The Library is for dragging and dropping assets from a document (as it says) - it's not for storing entire document files.
If you want to open a document file from your Creative Cloud files, click File > Open, then navigate to your user/creative cloud files directory, select the file and open it.
Creative Cloud files work by syncing the files to another computer which you have installed the Creative Cloud app on, to the Creative Cloud files directory on that computer, via the internet. You can also get access to the files via a browser if you log into your Adobe account on assets(dot)adobe(dot)com
The Library is also synced via the internet, on different computers. So if you have illustrator on two machines, the library on both machines will contain the same assets you dragged and dropped in there. You can also access your Library assets if you login to your Adobe account on assets(dot)adobe(dot)com