It is not to “clearly” visible to me that this is not a materialist anthropology. It was his explicit purpose in TGI to strip the concept of human nature of its ideal dimension, meaning Platonic, humanistic, moral, ethico-religious, unscientific “mystifications,” in order to reveal man’s species-being as a social animal, distinct from the other animals only in its capacity for (social) self-actualization through labor. Even in your own excerpt, our social relations are described in terms of relations of production (which can be more or less satisfying).

Is it perhaps this aspect of his thought which is preserved in the affluent, technological, society, and which brings alienation, as a lapse from an ideal, normative order of being, to its extreme pitch?

Ideal dimension did not mean "humanistic, moral". It can certainly refer to the religious dimension of the ethic, but humanism and morals are certainly not rejected by materialist philosophy! In fact, Marx drew heavily on Fuerbach, which was one of the most preeminent humanists. Perhaps the confusion lies with the idea of anthropological materialism, meaning materialism centered around humanist goals.

In the excerpt, social relations are not described as being only relations of productions, it's merely that relations of production are the ones being talked about. But it is clear to anyone that the relations of production are some of the most important and indeed most of our social relations are relations of production. But certainly, it's the non-material relations which are the focus here, not the actual product.

As far as the species-being of humans being only different from animals insofar as we can self-actualize through labor, this is a bit of a reduction. Self-actualization through labour, where labour is any productive act, done for any imagined purpose - it's more than the productive act, it's the creativity and freedom with which that act is taken that to Marx distinguish human from animal. Clearly this difference assumes to human a unique creative, free, conscious aspect, so while to Marx this is made evident through these creative acts, these acts differentiate us because they embody our creativity, consciousness, and freedom, not merely because of their product. In that Marx is no different from the humanists before him, he simply focuses on the expression of human nature on the set of all social relations that make it evident. The reason why he does this is because he believes that human nature expresses itself differently depending on the circumstance, and so that appealing on a Platonic ideal of human nature that is absolutely perfect and unchanging is incorrect, therefore he refers to species-being as the current embodiment of human nature.

To go back to your earlier point, yes, it is a way of understanding the human without any Platonic, religious, or mystical ready-made truth. But it is at the same time humanistic and moral. There is no denial of the freedom, the feelings, the subjectivity and the relationships of people, instead they are actually central, and they are instead understood through the material world where they express themselves. What is denied is the existence of a perfect, idealized, untouchable component to these things that is completely separate and inscrutable from the material world.

So if the objection to the theory of alienation is that it sees all social relations as ultimately based on "stuff", that is not the case, which is why Marx makes a distinction between social relations writ large and social relations.