Perfect Health Diet has a lot to say about this. Check it out for a great explanation, but I'll try to paraphrase:

Herbivores' gut bacteria ferment the fiber in vegetables into short-chain fats, so the majority of their calories come from fat. Can't comment on your quote, but carnivores tend to go for organs and fat before muscle meat. Long and short of it, most animals get the majority of their calories from fat.

Carnivores have short large intestines because the large intestine is essentially a fermenting chamber full of bacteria that digests fibrous matter. They don't eat plants so their need for a long large intestine is small. The place of fat digestion is the small intestine (for most dietary fats), not the large intestine, so having a short large intestine is not problematic to fat digestion.

We are most definitely NOT the only animal that eats a high fat diet.

Hyenas have some of the strongest jaws in the animal kingdom so that they can crack open bones for the marrow.

Carnivores typically "eat the guts out" before going for "lean" meat (if they even bother with the "lean" at all.)

And even herbivorous primates such as the gorilla derive the vast majority of their calories from fat, the only difference being that the fat is produced by bacteria in their digestive "barrel" rather than sourced directly from their food.

"This is also the case for herbivorous primates such as the gorilla. Even thought they eat a "plant based" diet, their gut bacteria turn it into short-chain fatty acids... The mean macronutrient can be broke down as fat=.05+.4, protein=11.8+8.2, available carbohydrate=7.7+6.3 and dietary fiber=74.0+12.9. Otherwise, 25% of energy as fat, 24.3% is protein, 15.8 % available carbohydrate, with potentially 57.3 % of metabolized energy from short-chained fatty acids derived from the colon fermentation of fiber (Popovich, etal, 1997)."

Don't forget zombies. They go for the brains and organs first too ;-)

All mammals eat a high fat diet

http://slowburnfitness.com/all-mammals-eat-a-high-fat-diet/

Generally larger prey animals have more body fat the larger they are. So the larger the predator, the more large prey it eats, the fattier the diet. Humans are fairly skilled at bringing down large prey.

I feed my dogs and cats raw, have for many years. The cats I keep fairly low fat - small prey (I buy mice, rats, rabbits etc, all are naturally low fat) usually, leaner cuts or small portions from fattier animals. They gain fat easily from more high-fat/high-cal foods, also my younger cat has had several episodes of pancreatitis following a very high fat meal so now I limit him strictly. My dogs I feed mostly larger prey, they have no problem eating large amounts of fat (occasionally) and their weight doesn't vary as much.