You seem pretty confused on the physics/mechanics of it. On a gas engine there is a vacuum created when you release the accelerator which requires force to continue to turn the engine via the drive shaft. The how is not whats causing you to skid its the amount of force. The force from a brake or the engine does not matter. I know there are conspiracy theorists online that suggest somehow its different but its really just the amount of force. Engine braking is a lot lower force than a hydraulic brake.
It all comes down to the friction between the tire and the road surface.