I hear an early statement in this video about "left anarchism" and a situation where competition is no longer necessary. I reject this notion, as even in a hypothetical garden of Eden where all physical resources are infinitely abundant, there is still scarcity of people's time and bodies; as there is only one of you, and only a finite amount of time you have to live to the fullest. Assuming nobody tries to force people into participating in group activities, they will find themselves needing to compete for each other's attention, approval, and time.
As such a capitalistic economy will emerge over the exchange of time and cooperation; take for example a situation of a group of friends who want to decide what to do for leisure on any given day, each has different tastes on what they want to do, but they all would rather do something together rather than alone. As such, the most likely outcome is that some of them will convince the others to participate in a popular activity, on the condition that they participate in activities the others prefer on the following days.
Some would argue that we are already close to such a state, as obtaining physical goods is almost trivially cheap in comparison to the price of services. For example, the price of even a luxury consumer good such as a high end computer can be gotten over the course of a week, and to a savvy consumer enough food to last a day is able to be purchased with funds obtained in half an hour of work; assuming they can find someone willing to pay the "minimum wage" of $10 an hour... However, people willing to pay $10 an hour for low skill positions are few, the price of people's labor is too expensive for even the rich to bother paying.
I myself had to calculate how much I'd have to pay to hire a team of only 6 people to work for a period of a year or two on a game development project, and the price of such a project approached millions of dollars; for nothing more than people's service. Effectively, the amount of capital required to even enter the market as a new producer is more than any single person could reasonably fund without significant contribution from others, either by patrons or investors. And again, the majority of the cost of the project would be in employees, the cost of all the physical assets required (multiple high end computers, various software licenses, electricity bills, and office space) were trivial in comparison, and could easily be paid for by working a second job.
Onto some shorter points, the moment you said "without leaders, but not without order", I could hear the Ancap who haunts the back of my mind groan in frustration; partly since the IRL version of that ancap is quick to distinguish that voluntary leadership is perfectly acceptable, as is voluntary heirarchy; people will naturally follow people who's ideas they agree with and who offer something of value to potential followers. What they have a problem with is coercion, in other words; what they have a problem with is rulers, not leaders; the distinction being that rulers control people through use of force.
... And no, arm twisting and taxation are not necessary; any service, including that of maintaining security, can be obtained through voluntary exchange. Moreover, taxation places a burden on all facets of society for the benefit of only a few factors; if taxes were taken primarily for roads, then you'd wind up with more roads than anyone has any desire to use, and people would have less funds to spend on things they personally desire; not to mention, the fact taxes are compelled means that the ones taking the taxes are not in anyway obligated to do a good job of fulfilling these services. Take the example of someone who after calling a council for years to get a pothole in a road filled, got fed up and paid a pizza delivery company to fill in the pothole and it was filled in the same day; even though the ones taxing her kept all the money she paid, in what the state would argue was for the sake of "paving roads".
Similarly, while Police are necessary, a Police funded by taxation is not. Private Police are viable, and in many places are already in service; their price being of course mitigated by the fact they have to compete with an even cheaper alternative to self defense in some of these locations; primarily that a consumer may simply buy a firearm for their protection if they cannot afford to pay someone else to protect themselves or their property.
To keep this comment from becoming an essay in its own right, I recommend reading Man, Economy and State, with Power and Market. From what I've gotten through so far, it covers much of what I've mentioned and more, though I seem to recall some other points I brought up coming from another similar book... But I forget which.
RE: [VIDEO] Does Pragmatism and compromise make me a Shit Anarchist?