This post is talking mostly about CSS and it shows a document object model tree. JavaScript is also used, given that he mentions React.
Among these options, it seems that Rust is most similar to JavaScript. But this whole article would be the same if React was written with Rust instead.
So what is the broken part of GUI development, and why is Rust positioned to fix it? As I see it, not much would change if we used Rust instead of JavaScript, except that it could be harder to diagnose when ReactInRust is being used.