The probability of player A being up a rook over player B is higher when player A is better than player B, even if their Elo is the same. So the author has picked scenarios where player A is already more likely to be better than player B but assumed they were of equal skill, which will cause the results to be biased.
If I have time later I'll try to whip up a small coin-tossing demo in Python that demonstrates what I mean, I'm definitely not the best explainer!
But I don't see how that wouldn't average out over lots of games?