At first it made no sense but then I realised that what the author is saying is that in a distributed system, when you make local changes, you do not wait for the changes to propagate to all participants and back to you, before your local state is considered to be consistent with the global state but rather it is considered consistent with the global state immediately even before your local changes leave your system. In other words, every change committed into the distributed system is immediately consistent with the global state even if there are undelivered changes as eventually all the changes produce the same outcome.
In a specific use case that might apply. For example, if two people edit the same document and fix the same typo, the visual outcome is the same, no matter who made the change first or last.
But that is very niche as if we would take a programming code, someone can change a line of code that someone else is changing as well and they might be the same, but then you have other lines of code as well that might not be and then you end up with a code that won't compile. In other words, if we focus on the singular change in insolation, this makes sense. But that is essentially never the case in distributed environments in this context and we have to look at broader picture where multiple changes made by someone are related or tied to each other and do not live insolation.
Either way, i see nothing useful here. You can "render" your local changes immediately vs wait for them to be propagated through the system and return back to you. There is very little difference here and in the end it is mostly just about proper diffing approach and has little to do with the distributed system itself.
PS: the problem here is not really the order of applied changes for local consumer, like in case of editing a shared word document. The problem here is if we have a database and we commit a change locally but then someone else commits different change elsewhere, like "update users set email = foo@bar where id = 5" and before we receive the other, later, change we serve clients invalid data. That is the main issue of eventual consistency here. As I am running a system like this, I have to use "waiters" to ensure I get the correct data. For example, when user creates some content via web ui and is redirected back to list of all content, this is so fast that the distributed system has not had enough time to propagate the changes. So this user will not see his new content in the list - yet. For this scenario, I use correlation id that i receive when content is created and i put it into the redirect so when user moves to the page that lists all the content, this correlation is detected and a network call is made to appropriate server whose sole purpose is to keep the connection open until that server's state is caught up to the provided correlation id. Then I refresh the list of content to present the user the correct information - all of this whilst there is some loading indicator present on the page. There is simply no way around this in distributed systems and so I find this article of no value(at least to me).