Santi, thanks for asking such an interesting and important question.
Can behaviour which isn't physically violent be abusive?
I think most people would agree that emotional abuse can exist without physical abuse; in other words, it's accepted wisdom that one does not have to hit a child in order for one's behaviour toward that child to be abusive.
The NSPCC defines 'emotional abuse' like this:
Emotional abuse is the ongoing emotional maltreatment or emotional neglect of a child. It’s sometimes called psychological abuse and can seriously damage a child’s emotional health and development.
Emotional abuse can involve deliberately trying to scare or humiliate a child or isolating or ignoring them.
Children who are emotionally abused are usually suffering another type of abuse or neglect at the same time – but this isn’t always the case.
Emotional abuse: At a glance, NSPCC
Here an adult recounts the emotional abuse that she suffered as a child: "Bawling at me, backing me into the corner until I was whimpering and crying, he would just laugh at me and walk away, satisfied by my distress." (NSPCC: Fiona's Story).
The European Union's Istanbul Convention defines psychological violence as "the intentional conduct of seriously impairing a person’s psychological integrity through coercion or threats" (Council of Europe Convention on preventing and combating violence against women and domestic violence, Article 33 'Psychological violence').
For the purpose of this answer, I'm going to treat the terms 'emotional abuse' and 'psychological violence' as synonymous.
'Punishment' versus 'consequences'
A lot of people (me included) would say that if their child behaves badly then the parent should enforce the consequences of the child's action (e.g. if you break your toy then you have to live with a broken toy, rather than having it replaced) and would differentiate 'consequences' from 'punishment'.
And while I think that's a distinction worth making, I would rather (in this answer) look at actual parental behaviours, rather than get too badly distracted by an issue which could devolve into semantics.
For anyone who wants to find out more about 'consequences' as an alternative to 'punishment', I recommend the Dr Sears website and books (e.g. "The Good Behaviour Book").
So can punishment/consequences exist without psychological violence?
Clearly one parent's 'punishment' could be another parent's 'consequence'. So what (if anything) is the difference between a non-abusive consequence on the one hand, and emotional abuse on the other?
Let's look at a more detailed definition of emotional abuse - this is the British government's definition:
The persistent emotional maltreatment of a child such as to cause
severe and persistent adverse effects on the child’s emotional
development.
It may involve conveying to a child that they are
worthless or unloved, inadequate, or valued only insofar as they meet
the needs of another person.
It may include not giving the child
opportunities to express their views, deliberately silencing them or
‘making fun’ of what they say or how they communicate.
It may feature
age or developmentally inappropriate expectations being imposed on
children. These may include interactions that are beyond a child’s
developmental capability, as well as overprotection and limitation of
exploration and learning, or preventing the child participating in normal
social interaction.
It may involve seeing or hearing the ill-treatment of
another.
It may involve serious bullying (including cyber bullying),
causing children frequently to feel frightened or in danger, or the
exploitation or corruption of children.
Some level of emotional abuse is
involved in all types of maltreatment of a child, though it may occur alone.
Working Together to Safeguard Children: A guide to inter-agency working to
safeguard and promote the welfare of children, HM [British] Government, March 2013
So I think the answer to your question is that if the punishment (or consequence, or whatever the parent chooses to call it) has the features listed above, then it is abusive.
And if it doesn't then it isn't. :)
Obviously this is only one definition of emotional abuse / psychological violence, OP if you had a particular definition in mind or if anyone knows of a better one, then please let me know in the comments and I'll try to incorporate it into this answer.
Clearly many of these things are a matter of judgement - for example, in defining what degree of protectiveness constitutes 'overprotection'. Where that's the case, I'd suggest looking at the effect of the behaviour on the child. If the parent's behaviour is causing "severe and persistent adverse effects on the child’s emotional development" then it is abusive.
If you know a child who you think might be being abused then you should contact the authorities and let them make the judgement. That's not a judgement that you and I (as non-experts) should be making. If you're think it might be abuse then report it. The NSPCC says:
Don't wait until you're certain if you are worried about a child.