Other comments are about how gorillas have guts adapted for digesting lots of vegetation. And that's true. But at its core, it's just that gorillas actually do eat a ton of protein.

They eat like 30 kg of food per day for 5000 calories, about 25% of which is from protein. That's more than 300 grams of protein per day.

Nothing they eat is super calorie dense, but the lack of density also means they need to eat all day. And as it turns out, the leaves they eat tend to be pretty high in protein.