Lessons from Ancient Mesopotamia
It seems a bit odd to attribute theories of state origins as coercion to Marx (I know in this case it's the 'hydraulic' theory of state formation that's motivating that thought) when I'd point instead to anarchist social theory (they even cite Scott) or for that matter to right-libertarian thinking.
There's one part of the interpretation that I'm not sure I understand, which is how they infer the novelty of the state in the cities within their study data. It seems it's via the appearance of an administrative building, but it's entirely possible that this post-dates the appearance of a "state lineage"--that the ziggurat's appearance is not at the same moment that a kind of lineage-above-the-lineages comes into being. (Indeed, given what they want to argue about the contractual character of the emergence of the state lineage, it has to precede the building of an architecture to match--this can't be a chicken-and-egg problem, because you wouldn't build an administrative structure prior to the appearance of a stable administrative social formation. But this is important because their argument hinges so much on timing--that state emergence is tied to fairly precise shifts in the river.
I think there's also a kind of naive understanding of lineages as being contractual rather than coercive or extractive. Economic historians who study African societies are quite able to point to examples of lineage-based political economies where lineages are intensely hierarchical and extractive, where you would never think to call agreements between lineage heads in a multi-lineage community anything like a social contract. There's a big problem with taking the basically liberal conception of personhood embedded inside social contract and applying it to societies where most persons would not in any sense be consulted or agree to decisions to form some new kind of high-level coordination of multi-lineage decisions. More importantly, in a society fundamentally organized around lineage, there is no "outside" the lineage--e.g., persons dissenting from the choices of lineage heads cannot opt out because there is no alternative form of social being available to them, no "stranger" status. Which kind of loops right back to theories that suggest the extractive nature of these early states.
(In that regard, it's a bit odd that they take no note of Scott's argument that early Mesopotamian walls are not the provision of public goods but instead a sign of extractive coercion--that those walls served to keep people in, not to keep enemies out.)
It seems to me they've got a good argument for the endemic rather than external origin of small states in the region (e.g., that these are not the extension of larger states like Uruk into a hinterland) but not necessarily for "states were created to solve collective action problems rather than to enable extraction".