This review is enlightening in describing Graeber's break from conventional anarchism in the Dawn of Everything. Early Graeber tries to make the best possible case for critiques of power structures that characterize our modern world or underpin its legitimacy --- critiques derived from or harmonious with those in conventional anarchist thought. I disagree with the author's interpretation of The Dawn of Everything as evidence of Graeber shifting toward liberalism.

The Dawn of Everything is actually a significant contribution to anarchist thought (though it may be fair to call it post-anarchism) because anarchism struggles to theorize and build alternative institutions that can sustain and protect an anarchist society from domination by external powers. Graeber's earlier idea of prefigurative politics provides a partial solution because one can experiment with anarchistic institutions within a capitalistic / statist society.

The Dawn of Everything implicitly addresses the limitations of prefigurative politics, which are obvious in practice. Prefigurative institutions that are not short-lived or small-scale are rare and typically grow their own ideosyncratic power structures e.g., the tyranny of structurlessness or Wikipedia. Although not approaching a "state" such structures make anarchists uncomfortable especially when they reproduce hierarchies from the broader society.

The Dawn of Everything teaches us not to equate domination with the state or necessarily with hierarchies either. The posted review takes issue with how late Graeber rejects the concept of the state. But this rejection in no way lets the state off the hook. The Dawn of Everything is unequivocally critical of the state and seeks to understand how the state stabilized and persisted as a world-dominating organizational mode. It pursues this ambitious, (and I think unaccomplished) goal by describing a wide range of early societies and demonstrating that some were violently coercive without state-like institutions (e.g., north american slavers) and that others were peaceful and egalitarian but had institutions that other work associates with violent coercion or state emergence (e.g., cities or agriculture). Then, by analyzing the stability of these societies and how they worked it tries to piece together a theory of decomposed types of coercive power. As the reviewer points out, this decomposition isn't that theoretically satisfying. There could be other ways than the three types of power, and some of the arguments around this part of the book in particular seem to stretch the evidence.

That said, it is useful for anarchists to recognize that just because a power structure or hierarchy emerge within a political project or organization that it is a failure. Opposition to the state and domination more broadly doesn't require commitment to design principles like leaderlessness or flat organizing structures. The book's most important contribution is to show that human societies have already explored a vast design space of political institutions in our history.

Anarchism has always been a "liberal" philosophy --- indeed the most extreme form of liberalism. Any state-socialist or communist will say this. It opposes the state because the state extended the scale and reach of coercive structures like conscription, taxation, and private property far beyond their pre-modern limits.
Yet the state is losing power to international governmental organizations on one hand and international corporations on another and so it is incredibly useful to think about ranges of better possible futures instead of doubling down on tried and tired commitments to ideological purity with a movement that was most significant and non-academic 130 years ago when the modern state was still contested in much of the world. Anarchism is stale but post-anarchism, like the Dawn of Everything, is essential.