It's funny how this newfangled "local first" thing is what us old fogies used to call just "applications."
I get that there is networking and integration that a modern application will typically need to do (depending on its core purpose), and syncing state to and from servers is a special concern (especially if conflict management is necessary) that native desktop applications rarely had to do in years past.
But at the end of the day, it sure does feel like we've come full circle. For a long time, every single application was "local first" by default. And now we're writing research papers and doing side POCs (I'm speaking generally, nothing to do with the author or their article) trying to figure out how to implement these things.
I feel this way at times too, but the ability to sync state really is key. Traditional native desktop apps rarely had to consider this because users would only ever interact on one device. Now users are moving between a computer and a phone, if not more devices.
If I were to frame it succinctly I would say applications = local-only which is distinct from local-first.