Yes, but if you uninstalled it on the desktop, then you have to reinstall it on the desktop.
Your laptop and your desktop are two different computers. Windows programs are not drag and drop; there is a formal "build" process called an installer that has to run. Even if you have all the files available in a directory, the Windows operating system on your desktop has no clue that they are there.
Now, it's possible to install FFXI directly to the USB drive or a flash drive. I've done it. But you still have to have the original installation file or CDs and run them, and then manually change the directory over to the external drive you're installing the game to. Why? because the installer file is what tells the Windows operating system where the actual game is located.
Copying the files from an installed system to a system where it was uninstalled or never installed is like handing someone a map with all the streets and buildings, but no numbers or labels. Windows looks at the folder you're asking it to run and says "I don't know what any of this stuff is called or where it is so I can't help you."