First of all, the speaker you quoted doesn’t seem to understand that there may be different types of power in the world. Mayhap there is direct vs. indirect power, active / inactive / reactive power, or known vs. unknown power, etc. Is power quantitative or qualitative, or both under certain contexts? Power is a general term and I conceptualize it as a “thing of force”. So then, it relates to a definition of “force” and onward and onward, until definitions stack upon numerous other definitions (that are changing) and you get nowhere without a pragmatic ideology. Therefore, the first problem with power itself is practically defining it so that it may be discussed by a group of intellects.
What is [power]?
For now, I will just say it is a “force that compels living beings to act in any way, passively and / or / nor actively”.
Thus, “is power necessary for order?”. Now there is the problem of defining “order”.
What is [order]?
Here, I will say that it is a “mental categorization of the human mind to act in a manner that is expected and especially anticipated”.
When things are “ordered”, then they are understood by the common human animal as “common sense”. Such actions are predictable, that people like to eat at McDonalds, that they like to drink Pepsi, that they like to defecate in privacy, that they like to watch television / use the internet, and that they will do these things where & when they are accessible and it is appropriate to do so. This is order, that certain things are expected, versus chaos, that certain things are unexpected. School shootings used to be unexpected and therefore “chaotic”, but since the mentality is now understood, people now commonly (unless I underestimate the public) understand how & why young male teenagers go and kill others and then themselves. Generally, they suffer from social nihilism along with tendencies for revenge against those “bullies” who wronged them. So, there is even an order to violence, once properly / commonly understood.
Is power (a thing of force) necessary for order (mental categorization of the human mind)? The answer is soundly “yes”. Forces occur with or without people knowing about them, so the implicit reason for any event to which we categorize it to make sense of the greater world must contain a context of power, or forces at work, in “order” for people to comprehend the event itself. How it happens is that a force impacts the mind to think in an environment of order (expecting what is predictable like the sunrise / sunset) vs. chaos (not expecting what is not predictable like your immediate death). Explaining these “forces” is the key to understanding both power & order and how they relate to each other, which is exactly what physicists attempt to do and describe on a daily basis. However, forces come in many shapes & varieties: physical force (to work), mental force (to think), spiritual force (to act), etc.
“So, is power necessary for order and if so, what sort of power?”
Power is necessary for order in the same way that it is necessary for every kind of thing, and it is the sort of power that uses “force” as its definition.
“What relationship does power have with authority?”
This can be a very short answer or a very long answer, but I will pick the short answer for now. If power is a “thing of force”, then must authority relate to force by definition? My answer is “yes”, because the meaning of authority is a “force that you must respect”. You may obey or disobey an authority, but regardless of that reaction to a command, the authority is necessarily respected by you. To claim that a person or thing is authoritative necessarily means that it should be listened to by any particular individual and there are supposed consequences for not doing so. The authority itself rests upon its “supposed consequences”, that if I don’t believe in Heaven / Hell that the authority of God is completely diminished by degree and as such, loses His divine authority.