Agree with the others that impulsivity and physicality are potentially maturity issues that are exacerbated by asynchrony, intensity, and sensitivity.

What is referenced in aeh's post linked above, however, is a different matter-- though they can SEEM like the same thing.

A lack of perspective-taking can either be a lack of experience doing it, or it can be a lack of ability to do it, or-- ominously-- it can be a deliberate CHOICE TO REJECT DOING IT.

Empathy is born on that perspective-taking, so getting to the reasons for it is crucial for knowing what to do about it with a young child.

I've seen firsthand what the latter sort of child becomes as a teen if parents ignore the problem or make excuses for why their child is not obliged to treat others with respect and compassion.

While I don't want to alarm you-- please reconsider justifying/rationalizing bullying type behaviors, or those that are interpersonally exploitative as "he's doing it because he's responding to the way that he's been mistreated." This is the precise defense that a peer used when my daughter encountered him-- and this person was an abusive predator in his teens. I don't know whether or not he was ever truly "victimized" (or if it had mostly been an affront based on his unmet-- if unrealistic-- expectations), but he was pretty committed to not giving any thought to empathy for others, and for exploiting and abusing them in any way available. His parents only saw him as the victim, btw.

Yes, I believe that there was pathology involved, and this child was quite frightening as a 17 year old HG teen. I have no idea what he was like at four, however.
Schrödinger's cat walks into a bar. And doesn't.