How does the code get inserted into the running application? Surely, this can’t work for a large number of domains of applications.
In the video, I think the REPL is an Emacs buffer backed by some extension that hooks up to a Clojure nrepl instance. When he saves the file, the webserver process reloads it without restarting. But you are right that this style of development requires the language runtime to support hot-code loading. Clojure and several other LISPs have this facility, as does Erlang.
Its a very common idiom with Smalltalk and other image based environments as well.