Thanks for sharing the photo. iTunes Match will work on an iPhone, iPad, iPod touch, Mac, or PC. Based on the photo, it looks like you have the iPod Classic. Since iTunes Match doesn't work on the iPod Classic, you'll need to find a different way to transfer your music.
If the music was downloaded from the iTunes Store, try these steps to redownload your music directly on the computer: Redownload music - Apple Support
If the music was downloaded from other sources, you'll need to search for a 3rd party app or software to assist with moving the music off of the iPod to the computer. You may perform an internet search to locate a suitable app/software to fit your needs.
All the best.