Clockwise versus counter-clockwise propellers and rotors are nearly irrelevant. They don’t matter to the performance of the aircraft. They only matter in a difference in flying technique. The Angular Momentum does not contribute to lift in a helicopter nor thrust in an airplane.
The site you reference in your question does not present any force of lift. There is no force implied acting parallel to the plane of motion of a spinning object. Neither the L (angular momentum) nor the omega (angular velocity) produce a force that will act upon an object outside of its frame of reference. In other words, they will not lift a helicopter nor push/pull an airplane. Don’t let the L fool you into thinking that it stands for Lift. It does not.
Take the weighted bicycle wheel attached to handles experiment as an example. Once you start the wheel rotating in open space, its angular momentum will want to keep its position (or at least direction) rigid in space. As long as you keep the handles pointed in a consistent direction, the spinning wheel will provide no force until it makes contact with some surface (torque). The wheel will not push nor pull the person or object holding it. Only if you apply force to change the position of the wheel’s axis (the delta in the equations), will the wheel apply a force to remain rigid in space. Or, it will transfer the force in a direction according to the direction of its spin (gyroscopic precession).
In real world application, this means that you can ride a bicycle without worrying about a force pulling you to one side or another. It is actually easier to balance staying upright the faster the wheels are rotating. You can even ride with no hands touching the bicycle. And, when you do want to turn the wheels, all you have to do is lean to one side or the other. Gyroscopic precession will turn the wheels for you.
Another example is how motorcyclists can stay upright without much motion forward. They rev the engine while engaging the clutch while relatively motionless or at extremely low groundspeeds. Revving the engine spins the flywheel attached to the crankshaft. The flywheel acts like a gyroscope. Again, this provides rigidity in space. It does not matter which direction the motor spins. All that matters is the rotational and angular velocity of the flywheel and the flywheel’s mass.
So, yes both clockwise and counter-clockwise engine-propeller/rotor combinations exist in aviation. The only advantages of one over the other is logistics, not performance.