> Failing to do so means that it has not learned a model of what chess is, at some basic level.

I'm not sure about this. Among a standard amateur set of chess players, how often when they lack any kind of guidance from a computer do they attempt to make a move that is illegal? I played chess for years throughout elementary, middle and high school, and I would easily say that even after hundreds of hours of playing, I might make two mistakes out of a thousand moves where the move was actually illegal, often because I had missed that moving that piece would continue to leave me in check due to a discovered check that I had missed.

It's hard to conclude from that experience that players that are amateurs lack even a basic model of chess.