First, I think that defining an mercantile exchange is important : we're talking of a product (either specifically produced in order to be exchanged, either coming from a surplus) whom ownership is considered desirable against another product of the same nature. Its usefulness is awfully relative : a bottle of water when drowning isn't the same than in an hot red desert).
A market economy implies a more or less formalized set of exchanges, guaranteed by customs or institution to at least allow the exchange to be made peacefully enough. Of course, such exchanges can be formalized as diplomatic ones,for example, allowing more mundanes ones to take place. Critically, these exchanges doesn't necessarily search a profit in the sense we understand it (critically not in non-monetarized economies) : these can be often called poltachs where gifts-giving can take the form of competitive loss for a social gain, but as well masking more "economical" exchanges behind.

Are these exchanges predominant in ancient societies? Not in the sense it is depicted there, but neither is the sheer subsistence economy. Indeed, relatively complex societies seem to blossom trough exchanges (think Wessex cultural network in Bronze Age compared to neighbours) as it increases the capacity of social mobilisation and specialisation overall, but its continued existence came to depend on these exchanges.
Did Bronze Age societies in Near East functioned on a systematized exchange and marked economy? No.
Did their existence depended of these exchange, and especially the supply of tin? Yes! (see 1177 BC of Eric Cline)

From examples I'm more familiar with, we could consider the decline of Halsttatian principalities in Central Gaul to be tied to the decline of Mediterranean trade roads and the Black Sea grain trade rivalling Rhodanian grain for a time.
Or the care of emerging Anglo-Saxon kings to provide for both basic needs and prestige goods in their political and territorial build-up (cf. Dark Age Economics by Richard Hodges)
The author doesn't really respects their own definition there : economy as a means to reproduce society, and not just economy itself.

When a community or a social group invests resources (would it be only human labor diverted from basic needs production) to build structures beyond the scope of sheer basic social-economic redistribution (let's say megalithic structures) it's something that doesn't address at all the question of food, shelter, clothing, means of transportation or means of production. From a strict economist viewpoint, it is wasted.
However, as a social and cultural expression, both reinforcing and changing society, it might be seen as primordial. Even in times of great crises, and even if its halted, such efforts are not only present but considered critical (Somptuary expenses in Late Roman Empire, when Romans are scrapping at money)
Furthermore,basic productions (for, say, food) isn't necessarily made with the goal of re-injecting it for consumption (with or without exchange) but rather as a social capital : for example, producing preserved food and holding it as reserve to increase its potential importance.

This is all the difference between, in Marxist terms, a simple market economy, which doesn't necessarily produces for profit, and a complex market economy where production is necessarily made in order to obtain a profit. (BTW, it is astonishing that someone claiming to channel Marx's spirit ignores which was a core principle of Marx's economical and historical thought). Conflating market and exchange with capitalism and wage-work is a mistake in this perspective, because exchange doesn't have to be socially systematized to be necessary.