The example code on that page just doesn't make sense to me.
In what way? Does it work for you?
It loads and compiles on the arduino and just plays every file it sees on the SD card.
If you want to hack that to only play files on your list then it is the void play(FatReader &dir) function you want to change.
The simplest way would probably be to include a check to see if the file it is going to play is the next on your list, if not you keep looking.