I'm curious about their claim to have "no loss in sound quality", when they say they're recording Spotify's playback and saving as mp3. I'd expect double compression that way (the original compressed audio from spotify, compressed again to mp3). Are they somehow reading the actual file as Spotify plays it rather than the audio, and saving that?

They say "Spytify records the same quality that Spotify outputs" but that implies a loss in quality if it's recording an mp3 and re-saving it as a new mp3. There's no lossless option in Spotify.

Spotify streams Vorbis format, so it's definitely doing lossy->lossy if it's saving mp3 files.