Is skin scratching disorder whenever the skin is scratched?

Not.
Many people will scratch their skin from time to time, which rarely becomes a serious problem and is not a skin scratching disorder. For example, itching is often associated with crusting as the skin heals, causing many people to scratch their skin.
In addition, many people also squeeze acne, blackheads and pimples and this is not usually a skin scratching disorder either. If you have other skin conditions such as eczema or dermatitis, you may also scratch your skin because it is itchy and uncomfortable.