Classic gambler's fallacy. Did you even read the wikipedia link above?
No that is not the gamblerīs fallacy. The gamblerīs fallacy is assuming that if you have not rolled a 6 with a normal dice the likelyhood of rolling a six increases.
The poster you quoted simply stated that not rolling a six has the probability of 5/6 with one roll, but 25/36 with two rolls, ... . With increasing the number of rolls the likelyhood of not having rolled a six converges against zero, while for every single throw the chance of not rolling a six remains 5/6.