An airplane's tires freewheel. Even if we count friction, just about every airplane, with the exception of the tractor plane in the original post, the wheels have low enough frictional and rotational forces to allow the plane to still take off. If the pilot can't seem to make it happen, cuff him in the back of the head and say the phrase "hey idiot, release the brakes"...
To test this, you'll need three things. A pair of rollerblades, a friend, and a treadmill. Your friend represents the engine of the plane. Have your friend stand somewhere other than the treadmill (i.e. off to the side). Start the treadmill, and have your friend hold you in position. Then have your friend advance the throttle on you (i.e. start pushing you forward to simulate the thrust an airplane's engine produces). You will not stay in the same place on the treadmill, even if you speed the treadmill up relative to yourself, you will still move relative to the ground, so you achieve lift (assuming a long enough treadmill, and a strong enough friend)...
An automobile or a tractor on the other hand, are driven by the wheels rather than an engine producing thrust, so therefore, these types of vehicles would have no ground speed relative to the earth or the treadmill.
Or you could go with the Harrier AV8, or the F35 joint strike fighter in development, and not bother with a runway at all.
That airplane in the original post looks like it's flying backwards though. I envision it as a twin engine pusher machine, where the propellers are in the back, with a canard in the front. Almost looks like some of the Rutan designs, except there's a tractor built into it...