The ransom letter is signed "Two Desperate Men." The apparent intent is to suggest that these kidnappers are capable of doing anything if the boy's father does not meet their demands. The word "desperate" is intended to suggest that they know themselves to be outside the law. They are already destined to be executed or gunned down for the terrible crimes they have committed in the past. But the signature might also suggest that they are in dire need of the money. If they don't get it from Ebenezer Dorset, they won't know where to turn next. Mr. Dorset might read his own interpretation into the signature. He might not be in the least intimidated by their broad hint that they are capable of killing his son. He knows, for one thing, that they are in more danger from Johnny (aka Red Chief) than the boy is from them. Mr. Dorset, knowing his boy so well, might understand that these two men are getting "desperate" because they have a tiger by the tail, so to speak. Bill and Sam have already had serious problems with the kid. For example:
Just then we heard a kind of war-whoop, such as David might have emitted when he knocked out the champion Goliath. It was a sling that Red Chief had pulled out of his pocket, and he was whirling it around his head. I dodged, and heard a heavy thud and a kind of a sigh from Bill, like a horse gives out when you take his saddle off.
Mr. Dorset remains very calm, cool and collected throughout this kidnapping experience. Like his son Johnny, he does not behave in the way he is supposed to behave. Johnny should be frightened and submissive, which he is not. The father should be overwhelmed by the fact that his precious little boy is in the hands of two desperate men. But Ebenezer Dorset apparently doesn't care much whether they kill little Johnny or return him. The two desperate men may have saved Dorset a lot of trouble by kidnapping his hellcat son. When the father offers to take Red Chief off their hands if they pay him $250, he is showing his negative valuation of his offspring. He is not behaving like a stereotypical father, any more than Johnny is behaving like a stereotypical kidnap victim. The whole story is based on this dramatic irony.
Bill and Sam continue to grow more desperate until Dorset's offer looks good to both of them. They have a hard enough time getting Red Chief to go back home and stay there long enough for them to make their getaway.
So the word "desperate" in the signature is unintentionally ambiguous and also unintentionally revealing. It is intended to suggest that the two kidnappers will kill Johnny if they don't get the ransom money. But it also suggests that they need that money badly and so are willing to negotiate, even though the letter says: "These terms are final, and if you do not accede to them no further communication will be attempted." And, finally, the signature confirms Ebenezer Dorset's expectation that his son will drive his captors to desperation.