If cats are obligate carnivores and require no carbohydrate in their diet, do they derive all the glucose their cells need through gluconeogenesis? Some sources I've found state that carnivores get their glucose from the animals they're eating, but that conflicts with the fact that they say cats and dogs require NO CARBOHYDRATE in their diet whatsoever. My guess is they just catabolize protein for energy and are better equipped to deal with the acidic waste products than humans are?
Obligate carnivore means they must eat meat (specifically to get taurine, which they can't synthesize), not that they can't also eat other things. In the wild, I've been told, some of a cat's nutrition may actually come from the stomach contents of prey. And mine have expressed interest in everything from broccoli to Graham crackers.
But it is certainly possible to burn protein and fats for energy. Humans do it too; where do you think the calories in a lean steak come from?
Nothing very special; basic biology.
(There are amino acids we can't synthesize too, but they're ones which are relatively easy to get from plants.)