Freedom of speech is a right that concerns you, a citizen, and public authorities. Censorship, in return, is when that right is interfered with by [the public authority] blocking your speech.
Moderation is when a [private entity] is blocking your speech. There is no public right that is interfered with in that case. You have the right to say what you want without public authorities interfering, but you don't have the right to say what you want in my house.
(Note: this definition is different from the one used in the article)
Whether or not Twitter is infrastructure, and therefore moderation equals censorship would be different debate.
In reality, freedom of speech is a principle that is more or less well-defined, and that is more or less codified into law in certain countries (the first ammendment to the US Constitution being the most famous example, but many countries have similar, though more limited, rights).
Viewed as a principle, it not only applies to the relationship between the individual and the government, it can be applied to all human groups. We can say that WeChat is worse for freedom of speech than Facebook, even though both are private enterprises and are not within the scope of any freedom of speech laws in most jurisdictions.
The reasons why freedom of speech is viewed as a virtue, at least in European-inspired thought, is not exclusively related to the relationship between the citizen and the state - it is about ensuring good ideas are heard even if that means bad ones are heard as well, ensuring that unpopular bad ideas of powerful people (within some group) can be challenged by the majority of the group, ensuring that minorities who are harmed by some decision get a chance to let everyone else in the group know about the harm.
These apply just as much to you vs the state as they apply to you vs your local church, your village, your tribe, your gaming clan, your company etc. For various reasons, each of these groups may decide that these reasons are not as important as others, while still wishing for some amount of freedom of speech (for example, a church will often not tolerate obvious blasphemy, but may still tolerate criticism of the church leaders, or vigorous discussion of the implications of scripture).
So, I am well within my rights to complain that my state or my company or my church or HN doesn't encourage freedom of speech enough, even though none of these institutions is bound by the freedom of speech clause of the US constitution. Also, I can even claim that the US constitution itself, or the SC interpretation of it, doesn't respect freedom of speech enough if I were to disagree with any decision on the matter - the principle of freedom of speech is separate from the US law.
I'm not an US citizen, and it applies to where I live as well, so there's that.
Within your framework, I agree with your views and conclusion though. My post was intentionally targeted as legalistic point of view, but I agree that this can be generalized.