I'm native Greek and this sentence seems to me like the dog eats the pork, in the sense that pork is its prey (unless there is en varg crossbreeding here). So, is there a difference in Swedish in saying that the dog or the wolf eats/ preys upon the actual animal as a whole? My hypothesis is that maybe you would drop the -kötten synthetic when not reffering to a single piece of meat or processed units from the animal's entity.
This is true sometimes. "Vargen äter älgen" typically means the wolf eats one animal, "Jag äter älgköttet" means a piece of meat. The kött-suffix is not always needed, one can say "Jag smakade älg igår" = "I tasted moose[meat] yesterday".
Though fläsk is only used for the meat. The animal, pig, is called gris. Same with nötkött that is only the meat, and the animal cow = ko. (Or "nötkreatur" in some contexts.)
That's not the reason in English. The words used for the animals come through the people who tended to the animals, i.e. the lower class. And the words used for the meats come from the people who were rich and powerful enough to regularly eat meat, i.e. the Anglo-Norman upper class.
So the words for the animals come from Old English, and the words for the meats come from Old Norman French.
It isn't really the case for Swedish, either. We use the same word for animal and meat in most cases. The only major exceptions are nötkött and fläskkött. In the case of nötkött, the word nöt is like saying "bovine" and ko is like saying "cow", so they just evolved in different directions. And in the case of fläskkött, the fläsk originally referred to a specific cut of pork, but gradually came to mean the entire meat.