The app uses the time it takes to go from (say) 5 mph to 55 mph to calculate the acceleration, and you enter the weight (also known as mass). The app then uses the formula Force = mass x acceleration to calculate how much TQ is being applied at the wheels (since Force and TQ are directly related).
Most dynos measure the torque, then calculate HP from the formula
HP = (TQ x RPM)/ 5200. Since the app has already found the TQ, it can plug that number into this formula to show HP. (Note: I haven't used this app, so I don't know if the app is reporting TQ/HP at the wheels or (by using a "fudge," er, correction factor) at the engine. A typical correction factor is 10% loss between engine and the wheels, but the true value varies from vehicle to vehicle and what gear the acceleration run is made in. If the app is reporting 272 hp at the wheels, the engine is putting out over 300 bhp (if the mass of 2200 kg is accurate). See below for more on that.
As you can see above, the app needs to have an accurate value for the mass of the car + passengers + cargo. If the mass entered into the app is too high, it will cause the TQ and HP numbers to be too high also (and vice-versa).