It's a concept called "Wild Gerechtigkeit" (literally: Game Justice). It's legally biding, but it formalizes the idea that you are honoring the game by hunting with the appropriate weapons, in an appropriate manner. Sure, there are issues with it: For example, an M1903 Mannlicher firing a 160 grain bullet doesn't quite make the E100 requirement, but one loaded with a 140 grain bullet easily will. I wouldn't want to be hit by either, and that 160 grain bullet has taken a lot of Red Stag. It's really no different than the requirement for .375 for Buffalo. Yes, Europeans tend to formalize common sense. The real pity is that it's sometimes needed.
Ah, here is the regulation in Poland (slightly different than Germany):
§ 3.1.
To carry out hunt and culling of animals posing an extraordinary danger
to human life, health or economy, only hunting firearms shall be used, from which,
after the maximum loading, no more than six shots can be fired; the magazine of a
self-loading gun may contain no more than two cartridges.
2. Big game hunting shall proceed, without prejudice to paragraph 3, only with
the use of hunting firearms with riffled barrel and calibre at least 5.6 mm and hunting
cartridges used for them with part-jacket projectiles, which at the distance of 100 m
from the muzzle have the energy of at least:
1) 2,500 J in the case of hunting elk;
2) 2,000 J in the case of hunting red deer, fallow deer, mouflons and wild boars;
3) 1,000 J in the case of hunting roe deer and young wild boar;
4) 500 J in the case of hunting carnivores;
3. The game referred to in paragraph 2, except for elk and stags, may be
hunted with smoothbore barrel, with the use of hunting bullet cartridges.
4. To carry out small game hunting, without prejudice to paragraph 5, only
hunting shotshells shall be used with pellet diameter of up to 4.5 mm.
5. Carnivores may be hunted with the use of hunting bullet cartridges specified
in paragraphs 2 and 3, hunting shotshells specified in paragraph 4, or hunting
cartridges with full-jacket projectiles.
Please note that in this case, the word "elk" refers to what we would call a moose (Alces alces).
Here's a good link. Others can be found using your favorite search engine:
https://huntadventure.pl/old/regulations.html