The conversations went like this:
PROMPT: Let's play a chess game. You start! e4 d5 2. exd5 e5 3. Bb5+ Bd7 4. Bxd7+ Nxd7 5. d4 Ngf6 6. dxe5 Qe7 7. f4 Qb4+ 8. Nc3 Nb6 9. exf6 Nc4 10. Qe2+ Be7 11. Qxe7+ Qxe7+ 12. Nge2 Qf8 13. fxg7 Qxg7 14. O-O Nd6 15.
RESPONSE: <played_move>15. Nxd5</played_move>
Most humans wouldn't even be able to play like this. Reasonably experienced chess players would play a lot of illegal moves.
The reason is that the encoding above requires cumulatively applying a series of actions to a two-dimensional model to which you apply rules that are described in a two-dimensional fashion.
It'd be interesting to see what the results would be if each prompt contained a two dimensional representation of the up to date board state.