Well, as your number one, go-to-egomaniac it's only natural I will share some of my thoughts about this topic with you.

Narcissists choose dominance. People who have healthy self-esteem, on the other hand, favour equality. In the same way that while narcissists adopt arrogance, criticism and denigration. Confident individuals go for humility, constructive feedback and respect individuals for who they are.

I very much disagree with this statement.
In my opinion, you can have a high self-esteem as well display a good amount of arrogance - without being a narcissist.
You don't need to treat everybody with respect and equality, if they don't deserve it. I don't have to respect brain-dead monkeys like religious people who are imposing their beliefs upon others, sometimes even threatening, hurting or killing them. Nope. Not a bit of respect and equality for these examples of human degeneration. And I can disrespect them without being a narcissist at all.
I treat people equally who deserve this kind of treatment. Well-used arrogance and denigration can be very helpful tools in dealing with certain kinds of people.

All this can be explained by the very fact that people presenting healthy self-esteem have built their confidence upon real achievements, deep moral values as well as care and respect for others. This is not the same when it comes to narcissists, as their actions are generally fuelled by insecurity, inadequacy and fear of failure.

Again, I disagree. You can still have a high self-esteem, but this doesn't need to be connected to real achievements. You can be very well aware of your skills, which are enabling you to actually do stuff - but even if you achieve much, your self-esteem might not be positively affected by it. For example, if you are a perfectionist, you will never be really satisfied with the things you have achieved, because there will always be something, which you could have done better. In this way, "real achievements" might even have a negative impact on your self-esteem. This is, why it's important, in my opinion, to disconnect your self-esteem from your achievements and focus on your actual skill set. You need to be satisfied with your own abilities and therefore your own personality and not with the things you did (not).

Besides that: I also don't think deep moral values are a key factor for high self-esteem. Morality is usually a quite flexible, fragile thing which mainly depends on your current social status and the groups you are belonging to. These things can change pretty fast. Attaching your self-confidence to your morality would make your self-esteem as fragile as moral values usually are.
Doesn't seem like a good idea to me ¯\ _ (ツ)_/¯