It doesn't help that the question contains a no true Scotsman type equivocation (most, relatively). This is, however, common to Wikipedia's coverage.
It also doesn't help that the comparison of social stratification between gather-hunter societies and, for example, late capitalism produces tautologies. Gatherers didn't wage-enslave the majority of the planet to the expanded reproduction of the value form.*1 Even gatherer societies, with differential production relations (class), cannot martial either the agricultural output or the down season labour*2 of early monument building class societies. Even amongst oppressed labouring class gatherers, the only social egality broken by different relations to creating wealth is gender. In a monumental society architects, master masons, and carpenters lack the egality of herdspeople, or field labourers.
To a large extent the question is answered through gathering producing no (or weak) ruling classes, and no specialist labouring occupations.
The equivocations being: gerontocracy; chiefs; priests, shaman, and magicians; and, of course the gendered social relations. Relative to heavily classed societies these are minimal variations—even compared to semi-autonomous highland agricultural communities with rigorous land egality cultures.
*1 the value form being capital and thus simultaneously wage labour and the commodity. We would recognise it as wage labour societies where labourers have no effective control over how production is organised, where commodities are produced for sale on the market, and where profit or Soviet-style growth whip firms into the pursuit of profit or growth.
*2 flood agriculture and agriculture in general involve periods where the work required is higher or lower. The period of lower work on crops is the down season. This is when a society can corvee or martial labourers to work on other projects like monuments.