Love the video! But, I'll be "that guy" for a moment (just for fun.)
I'll give the most important points of the argument, on why killing communist doesn't break the NAP.

What's assault? Assault is the threat or attempt to inflict harm on another's person or property. That is, a threat or attempt to violate the NAP.

How ought assault to be handled (justice vice)? For the practicality of a situation of assault, let's say a man tries to rob your wallet by pointing a gun at you, what should you be allowed to do in self-defense? You must be able to do the same - that is, to threat or attempt to inflict harm on the man's person or property, in the means of protecting your own. But it doesn't end there. If you were not allowed to act on this threat, or succeed with your attempt, the man would knew you were bluffing, and not be persuaded. Only if you were allowed to act on this threat, or succeed with your attempt, could you properly defend yourself.

How does this relate to communists? Admitting oneself to be a communist, is ultimately admitting that you don't believe others have a right to their just property (or that such thing even exists.) They claim that they can take your property, for either their own or others benefit, without having your consent - this is exactly what the robber from the previous example did. Saying that no one has a right to property, nor should be allowed to be in the possession of their property - and meaning one's statements, - is equivalent to committing assault. You're saying, that you wish - or intend - to inflict harm on another person or property, that is, to say that you wish, or intend, to violate a person's NAP - which is direct assault. Thus the person, which the assault is aimed at (which is actually every person owning property, which is every person,) or a third party acting to protect him, would be fully justified in mirroring the assault, and thus, as well, executing it; just as they would the robber. The communist would have to be physically removed, so to speak.