Chess implies a game. Conversations that are games already exist. It makes your idea dumb. Dumb ideas deserve no space.
Conversations that are not games are rare. That's an idea worth pursuing.
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I'm not afraid of games. I can play them if it is the only thing available. In fact, I can play the most terrifying role (for gamers): the role of ending the game and opening up space for reality.
The novelty would be a conversation platform that overcomes the primitive urge to game everything.