I'll give it a try at defining the author's intuition of "doesn’t cheat" in the sense that it is always "making real progress". I'll define it as every intermediate value that is generated in the computation is eventually consumed. If a function, say, computes Ackermann(5,5) and throws away the result and then starts the actual sorting process, then the Ackermann(5,5) is unused and would be considered cheating. In a sense we can draw a data-flow diagram of the computation and everything has at least one outgoing edge, except perhaps the final output.