Is there really such a thing as a post-scarcity society? Certain things will always be scarce. Beachfront real estate. Penthouses. Apartments next to a park or downtown. Sure we can get arguably get to a point where energy, food, and maybe small to medium sized items are free but if Jill Smith wants 400 cars where is she going to put them? Even if we all beam into cyberspace there will not be unlimited storage nor unlimited computation. There will still need to be a way to either get more from the powers that be for special needs or it will be traded leading back to have and have-nots.
Parent (and the article, although it fails to clearly draw the obvious link) could more accurately be said to be referring to a post-labor scarcity society.
In other words, a society where there is more labor available than we actually need to fulfill demand (caveat: in high-productivity industries).
To illustrate, take the article's example: the shift from an agricultural to industrial economy. Someone walks off a farm, they get employment in a factor. That factory worker can make 10-100 widgets / hr based on their labor.
Now look at the post-industrial economy we live in now. In software and heavily automated industries, the same single laborer can make 10-1,000,000 "copies" of their work product.
It seems fairly obvious there would be a breaking point at which productivity is so high that it disengages from driving demand. One worker can only buy so much, and his or her fellows can't buy anything because they're not employed.
This gets even more "extreme" when we talk about digital artifacts ... once the initial labor of creating a piece of music, or film, or game, or program is expended, the cost of infinitely reproducing copies of those approaches zero in many cases.