Making a computer have a 50% score against a 1300-rated human is way easier than making it play like a 1300-rated human.
For the former, you can take a top-of-the-line program and have it flip a coin in every game whether to make a random move every move or not.
Making one that realistically plays like a human is an unsolved problem.
Now that i think about it, i remember the people in the alphago documentary talking about the bot giving its moves percentage scores in both how high winning % the move had and how high % chance that a human would have made the same move that it just played. I wonder why they never showed what a full game of the most human-like moves from alphago would look like. Maybe it actually worked, by feeding it all the pro games in existence, and training it to play the high human % instead of the higest win probability moves like they did in the end.
What evidence lead you to think that, and how surprised would you be to be wrong?
I think the chess model would be successful at producing the desired outcome but it's not as interesting. There's something to be said for being able to write down in precise terms how to play imperfectly in a manner that feels like a single cohesive intelligence strategizing against you.
Despite decades of research, nobody has found a good way to make computers play like humans.
This means that the LLM does not actually have a lot of training data available to learn how a 1300 would play, and subsequently does a poor job at imitating it. There is a bunch of papers available online if you want more info.