As a note, I have not seen Gunpowder, so I can't say for certain how accurate their portrayal is. However, executions were both a common and public affair in early modern England. There was a very limited set of punishments available in 1605/6 that a convicted person could suffer. There is a lot to say about seventeenth century judicial punishments in England, so this is a rough summary. Fines and death were the two most common sorts of punishments. Banishment, branding, stocks, and imprisonment did exist, but were much rarer put into execution. Most often a person who was convicted of a felony (that is a crime which carried the death penalty) was either executed, found guilty of a lesser crime to avoid execution (often only punished by his stay in the gaol cell awaiting trial and a fine or bond), or pardoned. Executions occurred before crowds, often in the center of the marketplace, with lots of celebratory drinking and business occurring simultaneously. Court days & executions in the counties and towns were largely holidays, and the criminal was expected to perform. Convicts were taken to the scaffold or gallows in front of crowds, often being given wine or tobacco on the way. The convicted were expected to give a speech to their audience before being hung, often with last minute pardons being issued literally seconds before they would ascend to the rope. It was all part of the theater of execution, and the crowd was a willing participant.

The show might be taking it’s display of executions from the printed literature following the plot. Criminal literature was common in the seventeenth century, and would really take off after the Restoration. The Gunpowder plot was big news, so London printers tried to capitalize on the opportunity by published pamphlets on the King’s speeches in parliament, the trials of the conspirators, and even their executions. One such pamphlet was published in early 1606 that is easily accessible online in The Harleian Miscellany (12 volumes, 1808-1811) 3:45-52. After an opening stating his encouragement for papists to take heed, and decrying the intended crime, the author moves on to describe the execution of the eight men (Everard Digby, Robert Winter, Thomas Winter, John Grant, Ambrose Rockwood [Rookwood], Robert Keyes, Thomas Bates, and Guy Fawkes).

The author opens “Papists will perhaps idly say, it was a bloody execution; but in respect of their desert, in the blood they intended to have shed, it was a merciful punishment…” The author gives more intimate descriptions of each man, stating their demeanor, reputation, behavior in prison, and how they approached the scaffolding (site of their execution). Digby, Robert Winter, Grant and Bates were all hung, and no further punishment is mentioned (though their ODNB entries state that the four were also drawn and quartered).

More information is given for Thomas Winter, Rookwood, Keyes and Fawkes. Winter “went up the ladder, and after a swing or two with a halter, to the quartering-block was drawn, and there quickly dispatched.” To anyone in the seventeenth century, this description was enough, but it might not be familiar to modern readers. What this meant was that the man was hung by the neck until nearly unconscious and cut down. From there he was drug by a horse along the ground to an axeman, who would cut his body into four pieces (quartering) after disemboweling the victim. This was the fate of all four men executed together, convicted for treason and attempted murder. Further descriptions of the other three include (Rookwood) “hanged till he was almost dead, was drawn to the block, where he gave his last gasp”, (Keyes) “he turned himself off with such a leap, that with the swing he brake the halter, but, after his fall, was quickly drawn to the block, and there was quickly divided into four parts”, and (Fawkes) “his body weak with torture and sickness, he was scarce able to go up the ladder, but yet with much ado, by the help of the hangman, went high enough to break his neck with the fall…made his end upon the gallows and the block, to the great joy of the beholders, that the land was ended of so wicked a villainy.”

The last part speaks to the presentation in Gunpowder – “to the great joy of the beholders.” Catholics had come to be hated in the five decades between the accession of Elizabeth I and the Gunpowder plot. These men were not only heretics dangerous to society, but they had also attempted to murder their King, and place the English Crown on a Spanish head (or so the rumors went). The crowd at executions were typically enthusiastic about the impending death of the convicted; and in the case of the Gunpowder plot, they were perhaps more excited due to the extreme nature of the crimes the conspirators attempted to commit.