That's really good advice for anyone who has spotify regularly running on more than one computer. Your playlists are stored on all the devices that you have logged into. When you delete a playlist on one device that change will almost immediately update to the playlist server at Spotify, but the change won't update to other devices until you are online in Spotify wit them. So, get to your other device..
1. Make sure that the device is not connected to the internet
2. Open up Spotify
3. Copy the playlist URL, or drag the playlist title to your desktop to create a bookmark icon
4. Connect to the internet, and wait for the playlist to disappear, as the deletion update reaches that device
5. Paste the URL into the search box, or open up the bookmark
6. Subscribe (Yes - to your own playlist)
This is a bit harder if the second device is a mobile. In that case, go into Airplane mode in the device before opening the Spotify app. In this case, you can use the facility to Copy Playlist Link that you'll find in Share Playlist. Once your playlist link is copied, you can go online in your mobile and ..er.. email it to yourself.