Having attended specific "magnet" schools for G&T students for the entirety of my academic career, I'd like to think I'd have encountered at least one person who does this if it's really that common, especially among "mature beyond their years" children.
I don't believe that "disturbed" is the right word, but it does speak to poor communication and coping skills. That's not a personal failing by any means, but it does need to be addressed. This kind of behavior is much more common in toddlers or other not-quite-verbal children. It's not socially appropriate for an older child, and I hope the OP's son learns some more productive ways to deal with his frustrations with himself and the world around him. Childhood is tough enough already without (literally) beating yourself up.