I'll take a crack at it...
One of the biggest misconceptions about weight gain is that it comes from fat. Fat comes from fat. Weight comes from fat/carbs/protein in the form of calories. Most people (especially in America) have no problem getting calories from fat and carbohydrates. They're everwhere, hence we over-consume those two types of calories the most.
Breads, sugars, dairy, etc all give us more fat and carbs then we usually need. A protein diet lowers the excess fat and carbs are body intakes and you burn or convert that protein into muscles using exercise. Your stronger muscles then compound the effect since muscle burns fat and calories (virtually on its own).
The trick of the protein diet for weight loss is to mainly eat protein and skip the other two forms of calories. Stored fat and carbs will be burned away as you work out, as well as the protein (which will partially convert into muscle. So you gain lean muscle and burn fat/calories. What makes it a little easier with protein diets is... "generally" foods that are high in protein are low in fat and carbs. Red meat, not so much but eggs, fish, beans, shell fish, etc almost never have carbs and have low to moderate fat content.
But keep in mind the key to any diet is calorie intake... more important than what types of calories you ingest is the amount of calories... you have to burn more calories in a day than you consume otherwise you can't lose a lb because you haven't lost a calorie.
Any diet will "work" as long as you burn more calories than you consume in a day.