How many songs in total should it be? Because i can only see four and not the two you where talking about. But if it's a few songs you could use the trackset option in Play Button and add each song. You can read about here.
I can confirm looking at the playlist that the playlist does appear to have been created using local files which is why they are missing when you share the playlist. If you are building this playlist from the desktop client, the follow tracks must be imported into the client as local files (check the Local Files tab) as they have not been linked to tracks in the Spotify catalogue.
Jaheim – She Ain't You
Elvis Presley – She's Not You
Conway Twitty – 15 Years Ago
All of the other tracks have been linked to tracks in the Spotify catalogue but I assume they where also added to the playlist as local files.
I'm not using a device. Help me! I'm so confused. I'm just trying to get all the songs that look to be in my playlist on my computer to show up in the playlist when I import it onto a website I'm creating.