This sentence confuses me a bit. "The game of the teacher"? Meaning, they are playing a game in which they are pretending to be teachers(the teacher game)? Or does it better translate to the teacher's game? Ex. Teacher: "Hey students let's play a game!" .. Student: "I don't like the teacher's game". In my opinion, the answer provided doesn't make sense in English(US).
As mentioned in the intro to the Swahili course, both forms 'game of the teacher' and 'teacher's game' are accepted throughout the course. After all, they convey the same meaning. So this is just a literal translation, whatever the teacher's game really is :). Btw: Ninapenda mchezo wa viti vya ufalme :)