Ugh. Not a standard box plot. A bar graph with error bars (showing 95% CI, NOT standard deviation), or a boxplot with 95% CIs instead of quartiles is better. Standard box plots are only useful for deciding whether your distribution is normal or not (and a histogram is better for that).
The author also needs to do hypothesis testing to actually say whether any of the dice are diverging from fairness (which was his stated goal). You can't just look at a graph and guess. Your point that he should also test randomness is also good.