Whole leg smoked and salted like Spanish ham,
Intestines for sausages and black pudding, even cords if you dry them.
For me idea is great, because is easy to cook meat, but cook other (kidney, lungs, etc.) stuff to be tasty is harder, but you always get more dog food if you prefer.
Another thing is time, you need lot more time to butcher (whole day for elk), with do it in steps, it would be manageable in reasonable intervals and making carcass lighter.
Disembowel:
Drop to the ground - you can process it later for lungs, kidneys, liver. Eventually stomach, and small intestine for cords/sausage but it would take considerably more time and it easy to rot.
Pancreas and spleen is usually discarded, but it could be taken for dog food.
After disembowel - removing heart, then skinning - you can do it earlier with small game - warm carcass is easier to skin, but with big animals would be harder because of weight. Hanging carcass on tree could speed up the process, both for skinning and butchering. Additionally removing rest of the blood, as it makes meat spoil faster and not so tasty.
Then, you butcher the animal:
Front legs, hind legs, head, neck with shoulder, ribs, spine for loin, and lots and lots of fat under the skin.
Then you can cut meat from it, i don't know if it worth to make different meat and tendons, blood is very hard to get "on field" - it clots fast.
Same for bones, does it make sense to make more types of bones except skull?
Take brain out from big animal would be hard "on field" or very messy, but with sharp axe and trunk, one can easy get two halves
If I go hunting, and have no transport, with big game I will do disembowel, take heart and liver (if liver is not ill
https://en.wikipedia.org/wiki/Fasciola_hepatica ), skin, clean the skin to make it lighter, cut the legs, and tenderloins, leave the rest.
All above
It is much to wish for, but normally, after kill, you gut the animal, and took whole carcass home to butcher.