This is a follow-up to my previous post regarding the concepts of "acceptabiity" and "suitability" ( and that those concepts are not necessarily the same thing) of items of equipment in the EEM (or other GAF categories) ... unfortunately - as I mentioned elsewhere - the holster you are showing (while admittedly "old" in a general sense) definitely appears to be a Pattern 1937 Web Equipment pistol case -
http://www.karkeeweb.com/patterns/1937/1937_pistol_equipment.html .


Admittedly, that pattern is a re-work of the web pistol case introduced in 1935 for use, with Pattern 1908 Web Equipment, for the .38 Cal. No. 2 Enfield revolver. Its design also does bear striking similarities to another little-used pistol case, introduced with the Pattern 1919 Naval Web Equipment, although those were of a larger size, to fit the .455 Webley Mk VI revolver, and had a wooden nosecap. At any rate, those earlier (and relatively rare) versions also both come after the EEM cutoff year.
Perhaps more relevant than date, to the issue of "suitability", is the fact that this holster is a piece of
British Commonwealth kit, not really appropriate for use with the primary firearm you show ... namely, the U.S. Krag-Jorgensen rifle. To strive for such suitability, you'd want a U.S. military design of holster ...
Although perhaps of no interest to you, the balance of my comments will relate to the "period correct" British webbing and holster use in EEM matches The Pattern 1908 Web Equipment was introduced in the stated year for specific use with the newly adopted "Rifle, Short, Magazine Lee-Enfield" (SMLE). It has a distinctive appearance noticeably different from the later Pattern 1937 Web Equipment. Also,
there was no web pistol case design for use with the P'08 Web Equipment (at least not until the 1935 case mentioned above) ... rather, it was used in conjunction with the "Other Ranks Pattern"pistol case which had first been introduced into British service in 1877 … an open-topped, strap secured leather holster.

At time of original adoption of this type of leather pistol case, the standard-issue British military service revolver was the .450 Adams first introduced in the 1860s, but it was replaced at the end of 1879 with the .455 Enfield (aka .476 Enfield … this revolver was the "No. 1 Enfield" revolver that resulted in the entirely different .38 revolver adopted much later being called "No. 2".) Introduced at the end of 1879, it was a large, rather ungainly monstrosity of a handgun never very popular. (Note that the posted War Department List of Changes entry regarding this design of pistol case mentions that the versions produced starting in 1877 (to fit the smaller, shorter-barreled Adams) allowed the barrel of the new Enfield service revolver adopted in 1879 to protrude out the open bottom, and that the Mk II version was lengthened to completely enclose the barrel.) The Webley revolver introduced in 1887 to supplant the Enfield had a standard 4" barrel length (which remained standard through subsequent versions up to and including the Mk V introduced in 1913) so the majority of leather pistol cases of this type produced up to and going into WWI were the shorter version shown in the above line drawing. When the significantly different-looking Mk VI Webley revolver, with standard 6" barrel, was adopted in 1915 the pistol cases again began to be made in a longer version so the barrel would be completely covered.
Here is a image of Pattern 1908 Web Equipment in "Pistol Order" with this type of Other Ranks pistol case and
corresponding ammunition pouch ... both in leather -

If you did want such a leather British-pattern holster, moderately-priced reproductions are offered by What Price Glory:
https://onlinemilitaria.net/products/4610-UK-Leather-Webley-Holster/
From what I can see, only the "P'03" and "P'08" versions are currently available. Mind you, the ones I have (and the only version that I would order) is the P'03 version, which is the pattern of most holsters of this type from 1877 through 1908, having a simple leather loop sewn on the back for sliding onto any belt. If the wire clips on the back of the WPG P'08 version holster are aligned like they are shown in the WPG photo - i.e. set at differing levels, and not parallel to one another as they should be - I honestly don't see how you'd get the holster to properly fasten to a P'08 web belt … or any other type of web belt, for that matter ...