Yes, all streaming services require a membership to use their streaming players. 

The good news is that you can join Spotify for free here: https://www.spotify.com/us/signup/ 

Once you are logged into Spotify, revisit the playlist and you can stream it right there. 

Don't want to join Spotify? We’ve provided links to each of the songs on YouTube or Soundcloud (click on the song title in the playlist).