Those instructions tell you how to move media (as they say). A library is more than just media. For people using regular iTunes settings it is everything in the iTunes folder which includes the critical iTunes Library.itl file. This file generates the structure you see in the iTunes application. You need - Moving a library: Quick answer if you use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its sub-folders and files) intact to the other drive. Hold down the option (alt) key (shift on Windows) and open iTunes. At the prompt to create or choose a library choose the copied iTunes folder.
Note, I am leery about your "PC & Mac" compatible drive, whatever that is. While it is possible to use a FAT formatted drive with a Mac you have to realize that it has file size limitations and cannot be repaired with any Mac based tools.
What are the iTunes library files? - http://support.apple.com/kb/HT1660
More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management
What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html
Where are my iTunes files located? - http://support.apple.com/kb/ht1391
iTunes 9 [and later]: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847 - plus supplemental information about organizing to new structure https://discussions.apple.com/thread/6477809?answerId=26404702022#26404702022
Image of folder structure and explanation of different iTunes versions (turingtest2 post) - https://discussions.apple.com/docs/DOC-7392 and making an iTunes library portable.