Their training data is also part of their output. The training games produced last exceed the earlier games. So, yes, obviously the model can exceed its training data.

If you're trying to argue that the model can't be better than it is, i.e. the last training data it produces, then that's true but tautologically so. ML has conquered some domains, like Go or Chess or birdwatching, and is making progress in others - like programming. There is no reason to assume ML systems can't exceed human ability at programming or any other task.