going to Jerusalem vs child's game

As nouns, child's game is a hypernym of going to Jerusalem; that is, child's game is a word with a broader meaning than going to Jerusalem:

• going to Jerusalem: a child's game in which players march to music around a group of chairs that contains one chair less than the number of players; when the music abruptly stops the players scramble to sit and the player who does not find a chair is eliminated; then a chair is removed and the march resumes until only the winner is seated
• child's game: a game enjoyed by children