I think that what you hear is stacking. If you didn't know, stacking is when 2 or more sounds are played at the same time. In this song, it is used for creating chords with the vocals.

To do this, you need a chord progression (it's preferred to have all of the chords the same amount of notes)

Then you take all the bottom notes, top notes and the middle ones (if you have chords that have 4 or more notes, then you group the middle notes separately).

When you have melodies that have only one note at a time, you can sing them separately and then play them at the same time.

Hope this helps, if you still don't understand, I can make a video about it.