A better question would be if I agree or not...

Let's take what I believe is the uncontroversial meaning that to inflict means to cause.
Let's further assume the person making those statements is honest - ergo not lying, even to themselves.

"I will try to kill you!" we agree is a threat. The person saying it wants to cause death of the listener AND will participate in realizing that.
"I hope you die of cancer" is also a threat. The person saying it has no power to cause cancer and therefore can't cause cancer (excluding farfetched radiation poisoning situations I presume), but wants the death of the listener despite that lack of power to participate. Ergo intent to inflict harm YES, ability to inflict harm NO. More on this later...

"if you keep smoking like that, you could die of cancer" agree is not a threat, the obvious context is a warning and it would be a stretch to see any intent to inflict harm. NO intent, participation UNKNOWN (maybe the person saying this has no problem giving cigarettes repeatedly to the listener)
"if you jump off a building, you will die" likewise agree is not a threat, for exactly the same reasons as the previous. NO intent, NO participation possible.
"if you commit a crime, the police will arrest you" NO participation, but can be a threat (note I am saying can). It depends if the person saying it wants the listener to be arrested - if yes it is a threat just like the cancer example. If not then it is not a threat, and is similar to the smoking and suicide examples you made.

PS: On the last example, it was obvious from our conversation up to now that the first situation is what you had in mind. Even so I was careful to say can, instead of must. Because such a statement need not be a threat all the time. It just happens to be one given the context assumed by both of us.

Anyway the "I hope you die of cancer" is a better example to highlight our disagreement obviously. But then again, you were the one that chose the crime and punishment example earlier...

So, up to now, you were arguing that a connection is necessary between the threatener and the executor of the threat. Obviously in both the cancer example, and the crime example the executor of the threat is impersonal. In one case maybe it's fate or god, in the other it's the police or the state that inflicts the harm. You still argue this, saying, and I quote: Jamys would have no participation in the "justice served". As should be obvious I do not agree with you that this matters.

Now in this reply you also said, and I quote: jamys's statement was in no way an intention to inflict pain. This is a separate argument to the above, as I think is obvious that intent and participation are independent variables.

Now, according to the explicit definition I provided, intent to inflict, ergo intent to cause, defines the threat. There is no mention of participation - either participation, or lack of participation IF there is intent to inflict harm == a threat. If you still disagree with this, whatever the reason, please elaborate in more detail. In a way you already "know this" because in your smoking example participation, like giving someone cigarettes, does not create a threat on its own. The intent to harm is the key - participation is irrelevant. I don't think this is such a difficult logical distinction to grasp and hope it is clearer to you now.

Since you are also starting to imply more explicitly that jamys' intentions are somehow purely benevolent - with him having no intent to inflict pain - I want to question you further.

How can you read what jamys said, and not see a desire that an evil Nazi-like person should be punished? Is your identification with jamys' position that strong that you cannot consider the obvious facts and context of his post and how he wrote it? The wish to inflict harm is there. For most of the people his intent was implicit just from his unmerited insult / accusation of Nazism at klumpen. But he took it even further and made an impersonal and vague threat. His presumed lack of power to inflict said harm is irrelevant to establish the intent.

The fact that jamys believes inflicting the harm is for a greater good does not change any of that. In fact, IMO almost no one that inflicts harm on others is a sadist. They don't do the harm to derive pleasure from the other's pain. More frequently they do it to serve a greater good they believe in. Even most Nazis believed they were doing the right thing - because they believed nationalism, anti-capitalism and anti-Semitism to be good things. They were wrong.

You are also wrong in trying to push some weird interpretation of a threat where participation is required, but intent to harm is secondary. And further in believing that the lack of explicit mention about participation in the definition I provided means you can just imagine a logical AND is implied. In definitions there is no implication possible, by definition a definition is explicit. It implies nothing. So participation or its lack does nothing to define IF something is or isn't a threat. Only the intent to harm does.

Do you get it better now?
Because I have understood your points already. And you're still wrong.

Wrong about my definition of threat meaning what you want it to.
Wrong about jamys' intent.
Wrong that the opinions on display are enough to define most around here as Nazis.

But let's take one at a time. I have time enough and a passion to educate others.