They must be written to the disc - copying is writing to the disc. If you use Windows Explorer, you get the choice copying them as .mp3 files, or converting to audio. You get the same option with Nero, Roxio etc.
Assuming that you can see the files on the disc with your computer, it is possible the the disc could not be read in another computer because the disc wasn't 'finalised' and the second computer doesn't read discs which aren't finalised.
If you didn't finalise the disc, put it back in your computer, open Windows Explorer and right click on the drive letter. Select 'Close Session' and it will work.