You sound like an attorney, so I've got to call this out. Punitive, sure. But "a warning to others". Really? Is that an official legal concept in the US? Sounds unconstitutional to me, as I just said a minute ago in another post.
Obligatory and probably unnecessary disclaimer
I am a lawyer, but this is not legal advice and I am not *your* lawyer.
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As others have said, "general deterrence," meaning punishing one person for something to prevent others from doing the same thing, is a basic justification for punishment in the American legal system. It is generally accepted as a valid reason (although not the only valid reason) in both the civil and criminal contexts.
Second, "cruel and unusual punishment" is absolutely not implicated in this case. First, in order to apply, the punishment must be both "cruel" *and* "unusual." Even if you could argue that a large fine was cruel, which would be a tough argument to make, it would be very hard to argue that large fines are unusual punishments. Second and more conclusively, the prohibition on cruel and unusual punishments only applies to criminal penalties, not to civil penalties as here.
Third, there are limits on the scope of punitive damages under the Due Process clause, but it is highly unlikely that those limits would be applied to strike down a copyright judgment for a couple hundred thousand dollars. The cases where those have been invoked have usually been where damages were in the thousands of dollars and the punitive damages were in the many millions or billions of dollars.
Fourth, because this was a settlement, both parties agreed. That frequently involves waiving any claims that the demand of the other party violated the law-- after all, the point of settling is that both sides agree that it's better for them to stop litigating and be done with what they agreed to. If you can then continue to litigate, it kinda defeats the point. Even if they just concluded that going to trial would drive the legal fees up to a point where the settlement would be less bad, that's a perfectly acceptable reason for a settlement in our legal system.
Fifth, the fact that this might be something that a DA or US Attorney could prosecute doesn't mean that WotC didn't have a legal right to sue civilly. Let's say I'm walking down the street and John Doe jumps out of an alley and beats me badly, sending me to the hospital and costing me thousands of dollars in medical fees. Has he committed the crime of aggravated assault (or some such) or the tort (i.e. civil wrong, offense against me) of battery? Both, of course. I can sue him and demand payment of my medical fees, plus extra for pain and suffering and such. The DA could prosecute him for the crime. Those are really separate legal actions with relatively little interconnectedness (technically, there's a little-- if he got convicted in the criminal case, I could use that to prove my civil case, but not vice versa).
And if the DA chose not to file charges? Nothing I could do about it, except I suppose to support their opponent at the next election. So contrary to what others suggested, WotC couldn't force the DA or US Atty to bring a criminal suit.
That also means, incidentally, that the suggestion that the offenders could be facing prison time because of WotC's suit is wrong. You only go to prison if the gov't brings a criminal suit against you, and I've seen nothing suggesting that there was a pending criminal suit or that that played a role in the settlement. But the availability of large statutory damages does make the settlement potentially make sense from the point of view of the defendants. And the possibility of getting some payment, cutting off their legal fees, and getting the publicity of a successful effort to punish piracy makes it potentially make sense for WotC.