Radio Yerevan reports that: "In principle, yes, the photo is absolutely real. Except that it isn't a real photo, its name isn't 'England's Revenge in India' and the propaganda book never claimed any of that".
The picture in the question has a wrong description at the source, it is not a photo
The educational site German Propaganda Archive (GPA) hosted by Calvin College makes crucial mistakes in presenting the picture and describing it. In modern terms, the metadata is mixed up. (As utterly wrong as on the alamy.)
The original two pictures as published in 1941
If we look at the Nazi book, the mix up is evident, as it does not claim to show a photograph for "Revenge"; it has a different title and doesn't mention a magazine as source, originally:

click for large
(src for the last two pictures)
The picture on the left is titled "England's Revenge on India" "(Englands Rache an Indien)" and it is sourced as 'published by the Picture Post, 3 Juni 1939'. On GPA the caption for this picture is used in error to describe the "photo or painting" in question.
What's going on here with three possibilities in the question to choose from?
Just: none of the above from the three possibilities presented by OP.
The 'photo' on the right page 77 is the one in question and in the Nazi book titled almost correctly as "Execution of rebellious Sepoys" (Hinrichtung aufständischer Sepoys) and accurately described as being a painting by Russian artist Wassili Wereschtschagin. The English title Suppression of the Indian Revolt by the English is rendered in German as "Hinrichtung von Sepoys (1857)".
So in the original source we have only a reproduction of a painting for publication, correctly attributed. No claim that it is a "photo", and no claim to the effect of having found this in an English magazine.
The picture captioned "England's Revenge on India"
The actual photo titled in the book "England's Revenge on India", on the left of that double page, seems to be real:
Source of that image:
According to Sean Willcock, Postdoctoral Fellow, Paul Mellon Centre for Studies in British Art: "Colonial Photography in British India", September 21, 2015:

Image: Felice Beato, Two Sepoys of the 31st Native Infantry Who Were Hanged at Lucknow, albumen print from collodion-on-glass negative, June 1858. The J. Paul Getty Museum, Los Angeles. Digital image courtesy of the Getty’s Open Content Program.
Source attribution for "England's Revenge on India"
From where the Cigarette manufacturers got it for their Nazi propaganda book is unknown at the moment. But the claim that the Picture Post indeed did publish this picture with the hangings in mid-1939 is not disproven either.
The currently accepted answer was mislead into searching for a painting in the Picture Post archive despite the original source never claiming to have pulled it from there.
Whether the photo was also published in that magazine or not, we might find out in time.
Propaganda doesn't work if you just lie as you like.
Q Is the photograph “England’s Revenge in India” real, staged, or fake?
The photo with that title is real. But the photo with that title isn't pictured in the question. The picture from the question is a reproduction of a painting and properly declared as such in the question generating pamphlet. No mystery there, just an error in the German Propaganda Archive.
From a picture usage viewpoint the Nazi pamphlet uses on these two specific pages just the very same pictures as the current Wikipedia page for Indian Rebellion of 1857, and almost in the same context, directly together:

The whole propaganda book is online.
How did this error occur?
There are basically two possibilities:
The author of GPA, Bytwerk, might have just confused two pictures and their captions. But even more likely is that due to the nature of this book:
Raubstaat England started out as an exhibition in Munich. The pictures shown there were then distributed as cigarette cards and the 'book' is then really only a collector's album. An album with accompanying text by Ernst Lewalter in which each owner had to place the pictures by themselves. It stands to reason that Bytwerk was unlucky enough to work with a single copy in which the original owner misplaced the two images.
Timeline of Events
- 1857 — Sepoy Rebellion in India, British victory, and 'methods of suppression'. — No photo, not even a picture close to what's in question exists for the 'blowing of guns', but one photo of two rebells hanging from the gallows is shot by Beato.
1882 — Vereshchagin decides to go to India
[He] did not stay true to the word not to write any more war stories. This time he turned to the subject of the suppression of the British revolt of the sepoys in 1857. The Indian uprising of mercenaries against the colonists employers last but not least been successfully suppressed due to the public executions that received a poetic name "the Devil's wind." In 1857, the newspaper the People's Rares these highly effective interventions are described as follows:
"The British in India invented a method of execution so horrific that all of humanity is shocked. Are these merciful Christians invented a subtle way – tied living people to the muzzles of the guns, and then fired, ripping people to pieces, spraying blood rain of the pieces of the human body and guts at the audience".
1884 — The painter comments on the picture:
When (two years after the return of the artist from India) painting "The suppression of the Indian uprising by the British" was written, Vereshchagin commented:
"Modern civilization has scandalicious mainly to the fact that the Turkish massacre was carried out close in Europe, and then the means of committing atrocities too reminded tamerlanovsky times: cut, slit her throat, just sheep.Another thing from the British: first, they were doing the work of justice, the matter of retribution for the violated rights of winners, far away, in India; secondly, did the thing Grand: hundreds tied rebelled against their rule and not of sepoys of the sepoys to the muzzles of guns and no projectile, one gunpowder, shot them is already a great success against pererezali throat or ripping the belly".
Andrew Zimoglyadov: "The suppression of the Indian uprising by the British"
1939 — The 1857 photo by Beato is printed in the English magazine Picture Post (June 3, 1939, or not, verification pending!)
1939 — In Munich, Nazis organise an exhibition called "Robber State England", showing the painting by Vereshchagin:
, and the photo by Beato
1941 — The pictures from the exhibition are assembled for inclusion into a book of the same name with accompanying text from Lewalter. The book is made in two forms: one is a collector's album for cigarette cards as this was the way the pictures were initially distributed, another version has just the finished book with pictures already included. In this book the picture is accurately sourced as being a reproduction of the painting, not a photo.
post 1945 — Contents of the book end up as translated into English snippets, intended for showcasing German propaganda methods. Sometime at this stage pictures and captions from pages 76 and 77 of the book get confused and that error reproduced. At the latest. Perhaps one collector glued in the picture at the wrong place in the cigarette card collector's book version of the book.
~2008 — Randall Bytwerk uploads the wrong combination of Picture and caption to his page German Propaganda Archive
Sep 16 '17 at 19:35 — Prompted by the wrong caption (in some archives ) that now claims the Vereshchagin painting to be 'a photograph copied from a 1939 English magazine', this thread starts.