I thought you can't repeat a word? I maybe thinking too hard about this.
I don't think they are aware of that rule. At this point, call it a shouting match featuring the same word. I hope this helps you sleep at night
Tomato! Tomato! You're on! Tomato! Let's play shiritori!
A Japanese word game where the players have to say a word that begins with the last kana of the previous word.