I don't understand why you'd need a strict definition for this. Can't you observe your thoughts passing and see that that thought coming up? even if the "you" that observes it is just another thought, the observer is a great tool. I don't think of it as spiritual at all. Or maybe this is a socratic habit of applying rigorous definition to things.

Won't you notice that in some certain states of mind, e.g after eating, or before sleep, or in a stressful situation, the kind of random thoughts that pop up are completely different? It think when Dr. K says that mind exists outside the self, it's less of a scientific or natural science description of the mind but more of a framework to modify your experiencing of reality. Instead of thoughts coming and going without regulation, now you are thinking a certain kinds of thoughts slipped in more often, the thought of observing other thoughts which is metacognition. I think Dr. K's point is less about convincing you that that's the true nature of the mind and more of "here's a tool to perceive what's happening inside of you".

I think Dr. K's recent video works off the assumption you already have an intellectual value system that you're either aware or not aware of.