All depends on context.
Threats are a tricky thing. We must protect free speech and artistic expression. However, "true threats" are never and can never be protected speech. This is different from merely offensive speech.
Offensive: "You're a dick."
Potentially threatening: "I'm going to kill you, dick."
Offensive can be ignored, and should never be a crime. Truly threatening, however, cannot be ignored, and must be a crime.
But "I'm going to kill you, dick" is only potentially threatening. It also depends on context. If I said that to you right now, no one would believe that was a true threat. I don't know you. I don't know where you are. I have no reason to kill you. Even if I do know you and we're in the same room it's still not necessarily a true threat. Would a reasonable person assume I'm joking, or engaged in hyperbole? And not what you think. Doesn't matter what the person hearing the "threat" thinks. This is an objective test about what a "reasonable person" would think. This prevents a standard called an "eggshell observer."
So for something to be a true threat, a reasonable person would have to feel that they were in danger for their life or of personal injury. So lots of little boxes that you can check off to help add up to "true threat." Know the person? Check. Near the person? Check. Reason (legitimate or otherwise) to want this person dead? Check. Threat of specific action? Check.
His claim of "therapy" and "catharsis" don't fly. You cannot hurt others and say "no, it's fine, it's helping me." Perhaps what he finds cathartic is terrorizing others. The only possible way out here is "artistic expression."
So the question is, is this artistic expression? Or is this a sadist intent on terrorizing his ex-wife hiding behind the guise of artistic expression?
Elonis cited Eminem's song "Kim" as an example of what he was trying to do. In this song, Em graphically describes murdering his ex-wife, Kim. He's clearly talking about her, specifically. He says the specific horrific things he will do to her. He knows her, knows where she lives, and has cause (in his mind) hate her and want her dead. It's really, really close to a true threat.
Does anyone doubt that if, instead of performing the song, Eminem wrote it on a piece of paper and mailed it to her and her alone, that would constitute a true threat?
However, instead, Em recorded it and performed it for strangers. So I can say, in Em's case...artistic expression. But I don't doubt that thoughts of "is he serious? Do I need to fear for my life?" crossed Kim's mind. They would cross mine, and that of any reasonable person if someone they knew hated them that much said those things about them.
So somewhere between "mail a copy to only the person you say you want to kill" and "perform in front of millions" is the cut-off between "true threat" and "artistic expression."
Where does Elonis lie? I don't think he actually recorded or performed his raps. It was just on FaceBook. Which is semi-private. It would be easier to say "art" if it were on a public blog, open to anyone. But to say these things in a place where the vast majority of listeners know the subject, and it will certainly be passed along to her? Close. Close, close.
So were these "true threats?" Doesn't matter if he would actually do it or not, just something that a reasonable person would believe he would do. While yes, whether or not the recipient of the "threat" feels threatened or not is immaterial (no eggshell observers) the fact that so many people who knew him took the threats seriously (his boss fired him for threats against coworkers, the wife got a restraining order, his friends and family informed the authorities about what he was saying multiple times), it would seem unless everyone who knows him is "unreasonable," then a reasonable person would take his words seriously enough to act. So, I wouldn't have any difficulty saying that he did in fact communicate threats. Unless everyone around him is "unreasonable" and so is the jury who convicted him, then he communicated threats.
But was he intentionally trying to threaten? (did he want people to fear for their lives?) Or reckless? (knew people probably would fear for their lives and didn't care?) Or merely negligent? (truly didn't think anyone would take him seriously, and is therefore innocent. Stupid, but truly meant no harm?)
If I were the prosecutor I would argue that he was at least reckless. It's impossible to say that he didn't know people would fear for their lives. He got fired, his ex-wife got the restraining order, people called the cops on him multiple times. And the instant the FBI agent left his house after talking to him he goes back online and posts more of the same stuff! Whether he intended to cause people to fear for their lives or not, he clearly knew lots of people were fearing for their safety or the safety of others, and he kept doing it. He didn't care! Reckless!
There is this one little wrinkle. He did multiple times post between rants that he was not serious, was no threat, and was just using this as artistic expression and "therapy" (which he sorely needs).
So if I were the defense, I'd argue that yes, he knew people were fearing for their safety. Which is why he posted disclaimers that there was no seriousness behind his words. This means he had no guilty mind. He knew people were bothered, and took steps to assuage their fears. He was, however, too stupid to realize they'd still be scared. He should have known better. And this makes him merely negligent, and not criminal.
Then it would be up to the jury to decide if his protestations outweigh his threats.