Do you think it's possible we'll get to the point where technology makes labour so cheap that capitalism and markets as we know them now will no longer make sense?The short answer is yes I do - in fact I'm betting on it.
The functional problem however is distribution of resource production/demand. A functional market requires that some Agent A has some resource X that they can trade with Agent B for resource Y for some exchange rate. The medium of exchange (currency) is an important aspect to the efficiency of this but is too complicated to factor in to this discussion.
If the plurality of Agents do not have a resource that is in demand then they have nothing to trade and thus their optionality is severely limited.
For all periods of time individual labor was the default resource that people traded. Either they traded it to themselves in the form of time for output of land (farming for ones self), they traded it for goods from someone with those goods, or they traded it for a medium of exchange (currency).
If the "market" effectively drives the price of labor to 0 then the productive input for any Actor basically evaporates. That doesn't mean the market evaporates, it simply means that individuals have no pricing power inside of it. So the idea of your average individual controlling the means of production is put into jeopardy - which I think is what the Author meant to say.
Ok, so then what? Well that's when you see projects to redistribute resources to Actors with no pricing power introduced - such as UBI. Such schemes however rely on an increasingly small number of Actors to provide the resources which are then redistributed into the system. The libertarian proponents of such systems assume that the small groups will voluntarily redistribute these resources, which could be the case. Pro-state proponents suggest making the state redistribute the resources - essentially ending the "capitalism" - though the author doesn't suggest this.
I think functionally this redistribution at scale is impossible with the human animal. IMO the human desire for unfettered agency is too strong to accept such a construct.
I'm not sure what the answer is but I think it's gonna get nastier before it gets better.