There is 15 files on the disc and one called desktop.ini that says “files ready to be written to the disc” that will not copy over.
desktop.ini is a hidden Windows file that saves the location of items on your desktop. It has a protected status in the operating system, which is why it won't copy. It shouldn't be on the game disc though. It sounds like you copied the files to your desktop before attempting to burn them to a new CD, and desktop.ini wants to come along for the ride.
I got rid of my XIII CDs when I bought the GOG copy, so I can't check for sure. But I suspect that burning just the files won't work. Given the era the game was released in, I would expect copy protection would prevent that. In order to get around that so that you can keep your original discs as an archive, you will probably need to use disc imaging software to burn a 1:1 duplicate of the CD. Doing it that way will also prevent stray system files from finding their way onto the target disc.