The gradual simplification of the melody may be due to the fact that it is after all a children's song; it may have been altered for pedagogical purposes, i.e. to suit the faculties of kindergarten-age children. In any case, the fifth interval that rules both extant tunes is typical for text-oriented songs and thus fits the use of the song as a game.
The melody's simplification could be attributed to its being a children's song; it might have been modified for educational purposes, specifically to match the cognitive abilities of kindergarteners. Regardless, the fifth interval that governs both versions is typical for text-based songs and thus fits the game's use.