Is the same processing step not happening here?
To my mind the argument against this model qualifying as a language model is that while the sequence of tokens may technically qualify as a sort of language it doesn't appear to be generalized by any reasonable interpretation. Further, the model doesn't appear to be able to handle unstructured inputs and outputs in the "language" - everything seems to be highly structured.
My line of reasoning could be approximately summarized as compiled binaries constituting a "real" (though not natural) language versus a sequential listing of chess positions that represent sequential game actions only being language "shaped".
Still, it's interesting to consider that if scaled up I expect the "repeat yourself" experiment would likely apply to the internal representation of the model in the same manner.
The distinction is meaningful because the process described here isn’t bound by the same constraints, resulting in meaningful consequences.
Suppose we flipped the initial stings and fed that into the process. There would still be meaning to extract from the training set but our new Reversed English but it is not English so the preprocessing step can’t be based on that assumption.