It seems that it only uses notes on a pentatonic scale similar to playing up and down the black keys of a piano. That's something I often used to do when I was a kid, because it does usually sound good!
As to why it sounds good, there's no definitive answer (and of course to some people it may not sound good!) but music that is harmonically pleasing to most people will tend to have lots of occurrences of simple frequency ratios between notes that make up the piece, especially when those notes are playing at the same time. This happens to occur a lot when you choose even fairly random selections of notes from this particular pentatonic scale. (For related reasons, you could see this scale as made up of important notes in the minor scale - a bit like a blues scale in some ways).
Unfortunately there may not be not much more mileage in that specific idea, because there is a limited number of simple ratios you can use - anything else you made with the same pentatonic scale could end up sounding similar to 'plink'. However, if you take the general idea of providing a set of musical options, all of which sound OK, and then allow the user basically just to select which one to choose, there are lots of routes you could go down. For example, you could have a similar 'game' where one 'player' was selecting the root note of a chord from the major scale, and another was picking which note in the chord to play in the melody.