It's not executed in-browser, it runs in the Swift Playgrounds app. Think of it like an RSS feed that you can add to the app, and it'll show you new chapters of the book once they're published.

If you're interested in it you can compile swift to wasm (webassembly) which can run in the browser natively

https://swiftwasm.org/

This won't be it executing editable Swift like on the website and it'll require some binding to send and receive data to the website but it will indeed be swift being executed on the website

Browsers can't execute Swift code. The books are loaded directly into the Swift Playgrounds app.

As for links, there are very few subscriptions published – and probably none yet that work with Swift Playgrounds 4.0.