It's not about nostalgia. This device generates very different sensations. There's something very solid and immediate about having your music on a CD. Though services like Pandora or Spotify promise limitless access, perhaps you don't really need "the whole world of music" at your fingertips. Even if it's somewhat winnowed down with dedicated music devices like the iPod, which has limited storage, there are still too many choices and endless scrolling.
With the CD, you choose an album and settle down to comfortably listen to it. I like the sensation of pushing "forward" or "reverse" on a player; it feels more real, more responsive. There are a set number of tracks, either as part of an artist's selection, or one that you have assembled yourself with a CD mix. Like a book, listening to the CD is a complete experience: it has a finite beginning and an end.
I listened to the new Taylor Swift album 1989 on my CD player, during a BART ride yesterday. It was satisfying. At risk of seeming old school, I think I might walk around with this as my music player for the foreseeable future.