Alright... I'll bite again.

The wheels of the airplane are simply there to support the air craft and to allow the plane to roll as it accelerates.

For the plane to have thrusting force it simply relies on air to make it happen. Have you ever seen a jet powered dragster? Well it's the same concept but with wings and different aerodynamics to allow it to fly, that's all.

Whether ground is at stand still or moving (treadmill) has no effect. Theoretically, forces of gravity aside, if the plane or the dragster were suspended in mid air standing still, then thrust from the jet engine would be applied, both would still have momentum in the opposite direction of thrust.

Think of it this way. Shuttle is taking off into space. Now, let's say shuttle is taking off vertically but the wheels are resting against a wall of sorts, no matter which direction (forward or aft) the wall is moving, the shuttle would still take off. Essentially, it's just like the plane on the ground/treadmill, but at a 90 degree angle.