When you come to a stop with a manual transmission you have to push the clutch in or take it out of gear to keep the engine from stalling out. What keeps the engine from stalling in an automatic transmission. Even when I rev the engine while holding the brake the engine won't stall out, I can tell the car is in gear because it's trying to move forward but the engine stays running. If I tried this with a manual transmission the engine would stall
The reason that an automatic doesn't stall out while "in gear" and at a stop, while a manual transmission does, is that automatic transmissions use a hydraulic torque converter to connect the engine to the transmission, while manual transmissions use a friction clutch. These two systems do a similar job in a very different way.
A torque converter uses fluid to transfer the power, and so it can "slip," effectively disengaging the engine from the drive wheels at low speeds. When you come to a complete stop in an automatic transmission car, the torque converter starts slipping, allowing the engine to keep turning even though the wheels have stopped.
The only way to get the friction clutch of a manual transmission to slip is to depress the clutch pedal. If you come to a stop in a manual transmission car without depressing the clutch pedal, the engine stops turning when the wheels stop turning, and the car stalls.
It is important to note that revving the engine on an automatic transmission car while holding the car stationary with the brakes causes premature transmission wear and early failure. This action causes the fluid to overheat. It also damages the torque converter and driveshaft or cv joints.
If you look at advertisements for performance torque converters they will mention antiballooning,furnaced brazed fins and roller bearings. These are all needed if you want to abuse the drive train by stalling the transmission with the brake. By pressing the brake and the gas pedal at the same time it is possible to spin the tires. The technique is as you described.