The post treats reconstructive transmission as compatible with a replicator class: patterns can still be selected at population level even if they are not gene-like copies. Dan Sperber's claim is stronger, and it is the competing model.
In Explaining Culture (1996), chapter 5, and then in "An objection to the memetic approach to culture" (in Aunger's Darwinizing Culture, 2000), most cultural items are produced again, with a causal link between productions, but they are not copied from one another. Replication, when it happens, is a limiting case of zero transformation. Stability comes from cultural attractors: psychological and ecological biases that pull reconstructions toward the same region of possibility-space, so the variations cancel.
The demonstration is small. Ask people to copy a familiar five-pointed star from memory, then copy the copies. The star holds. Ask them to copy an unfamiliar squiggle the same way. The squiggle falls apart. The star was not transmitted with gene-like fidelity. It was recognized and drawn again. Little Red Riding Hood is the same point at story scale: if you only heard the ending where the wolf eats everyone, you either don't retell it, or you put the huntsman back. The first is selection. The second is attraction. The story is still here because of the second.
Dawkins already flagged this in The Extended Phenotype (1982): cultural copying is less precise, blending happens, mutations can be directed, Lamarckian arrows run from the thing you see back to the thing you pass on, and "these differences may prove sufficient to render the analogy with genetic natural selection worthless." His later reply, in the foreword to Blackmore's The Meme Machine (1999), was that the instructions are self-normalising, so the fidelity objection mostly goes away. Sperber's objection is that self-normalising is attraction doing the work, which is not a defence of replicators. It is a different engine.
The post's host-and-horizon audit can sit on either engine. It does not tell you which one is running.
Boyd and Richerson never needed the gene analogy. Culture and the Evolutionary Process (1985) splits three forces that the post folds into one word.
Guided variation: people transform what they receive toward something they already tend to produce. That is Sperber's attractor, written as a transmission force. Biased transmission: people preferentially adopt some variants — because of the content, because it is common (conformist bias), or because of who already has it. Natural selection of cultural variants: people who carry a variant have more cultural offspring. Those are different machines. They can point different ways.
Henrich and Gil-White (Evolution and Human Behavior, 2001) is the discriminator the post does not run. Prestige is freely conferred deference that evolved so learners could pick good models for information they cannot evaluate directly. You copy the person who looks successful, including packages that did not make them successful. Dominance is force. Prestige is not.
They disagree with a meme's-eye view on a cheap observation. Change who is high-status without changing the variant's wording, and prestige bias moves the distribution. A replicator model moves the distribution only if the variant itself got better at copying. That is a prediction, not a mood: find a written value-formula that stayed put while the people copied for status were doing something else, and see which distribution moved.