If I throw a fair die 10^6 times, the probability of getting any given single outcome should behave according to Poisson statistics. On average, if I repeat a trial of 10^6 die-throwings many times, the number of outcomes of "4" (let's say) should be on average 10^6/6 = 166,667 , as mentioned in the article.
However, the exact number of times "4" comes up in a given trial itself follows a distribution around that average whose spread is about sqrt(166,667), or about 400. So the typical "error" in the frequencies given in the table should be ~few hundred.
By this reasoning, the deviations in the top table, the one given by the primes, are surprisingly small -- of order tens rather than hundreds. In other words, primes are more equitably distributed among congruence classes than we would expect independent die roll outcomes to be.