I got the Barnes & Noble exclusive edition a while back, and yes, it does have extra content! It includes a few full-color illustrations of key scenes, which are stunning and so, so dark—perfect for the tone. There's also a brief note from the author at the end reflecting on the writing process for 'Manacled', which I found really interesting since it started as a Dramione fanfic. The hardcover itself feels substantial, nice paper quality. No extra chapters or extended scenes, though, just the art and the author's note.
I've seen some people online hoping for deleted scenes or something, but the extra material is purely supplementary visual and commentary stuff. If you're a collector or a big fan of the fanart surrounding the story, the hard copy is totally worth it for those illustrations alone.