Logikal might be correct when he says that this is not an example of a fallacy in general. However, the manipulation of words is a huge scam that can arguably veer into the realm of fallacy. It is certainly something that philosophy students should be aware of, particularly because many of the scammers call themselves philosophers.
Case in point - conspiracy. I'm working on a book about conspiracy science, and I was floored by the new definitions of the terms conspiracy and conspiracy theory that have been coined by propagandists. In fact, I've written five separate chapters addressing this topic alone.
Merriam-Webster features just one definition for the term conspiracy theory. It's an example of what I call the classic, or traditional definition.
Dictionary.com is a relatively new operation that offers three definitions. The first defines conspiracy theory as a theory that differs from the "standard theory."
Many propagandists define conspiracy theory as a theory that differs from the official theory - a bit of a problem if there's no "standard" or "official" theory to begin with. They further argue that the government and media are trustworthy sources...and therefore they must be right. (That is a classic appeal to authority, which is a fallacy, by the way.)
It has also become popular to define conspiracy theory as a theory that's inherently kooky. This would appear to be treading awfully close to an ad hominem attack, which is considered a fallacy. Indeed, a popular meme among propagandists is "conspiracies are for losers."
Taking it to an even greater extreme, some propagandists claim that conspiracy or conspiracy theory don't even exist. (Karl Popper conceded that conspiracy is real enough, but he claimed that it's exceedingly rare and - on an even weirder note - we shouldn't talk about it.) The reason is that they don't meet the criterion of whatever obscure definition they're using.
As discussed in the Internet Encyclopedia of Philosophy's article Conspiracy Theories, some philosophers have divided philosophers who study conspiracy into two groups - generalists and particularists. The former group believe there's something about the term conspiracy theory that automatically impeaches its credibility.
So two people could have the same theory, but if one calls it a "conspiracy theory," they may be ridiculed. But if the other calls it a "hypothesis," they should theoretically be treated with a little more respect.
An author may make some wild claim about conspiracy without telling the reader what definition he is using (a lie of omission), or they may explain the definition in a manner that makes it hard to understand (obfuscation). Of course, neither lies of omission nor obfuscation qualify as fallacy, however.
The terms fascism and genocide are similarly manipulated for political purposes. It's gotten to a point where some argue that both words have become meaningless.
However, your specific question seems different - and a little confusing.
You wrote that people who criticize journalists and the media often make false statements and accusations, noting,
In US Constitutional Law, false statements of fact are an exception to
the protection of Free Speech under the First Amendment.
Surely, you're aware that the media do the same. For many people, the word "media" is virtually synonymous with liar or deception.
Of course, two wrongs don't make a right, so that doesn't necessarily render your comment invalid.
However, another question revolves around the meaning of the word "attack." In the example you gave, an individual may have offered a bogus definition of attack. On the positive side, they at least spelled out how THEY define attack, although they apparently didn't offer a source or many details.
To me, the issue is either finding a definition you can both agree on, or letting the other person know that you don't accept their definition. (You might press them for details, asking if their definition has some kind of legal standing, for example.)
This statement is a can of worms...
If you’re saying that ‘free speech’ is an ‘attack’ then you have a
problem with free speech."
In addition to defining "attack," we also have to define "free speech" and explain how it works. Since media rats (to use a relatively polite term) lie on a daily basis, it seems only fair that people lie about them in return (although I don't recommend it). And if someone wants to claim that a media critic in attack mode isn't engaging in free speech, then that argument should also be applied to the media.
I loosely define free speech as the legal right to say whatever you want to say, whether it's true or not. (There are, of course, some exceptions, like yelling "Fire" in a crowded room when there is none.) Free speech gives people the right to lie, and if you disagree with that, then you're condemning politicians, the media, corporate executives, lawyers and lots of other people.
Instead of focusing on free speech, you might want to consider the term fair speech.
Going back to your opening question, I strongly suspect that using re-engineered words or bogus definitions does qualify as a fallacy. Maybe someone else can shed some light on that question.