Aren't "local-first apps" in this context the ones where you vist "example.com", and it caches a bunch of HTML and Javascript and saves data locally using the "local storage" APIs? And then periodically makes requests back to "example.com" to check for updates, sync data, etc.?

Kinda yes kinda no? Most PWAs have some idea of offline support but it tends to be an afterthought. The argument of local first is that you design the app to work against a local database ( normally stashed in indexeddb or OPFS ) meaning that you don’t have to wait for data to load or network requests to complete. Your backend is then just a dumb storage engine which accepts changes and sends push messages to the client to indicate things have changed.

The only “big” local first app I’m aware of is Linear.

While I hesitate to agree with that definition of local-first, I agree with your notion thats what the author by large is talking about and unfortunately many such an web-app have the worst of both worlds.

Most uses of the term local-first I see regularly mean to say, "an app that doesnt require 3rd party servers outside of your control to function", within some level of reason. Sometimes agnostic to how it's data is synced, sometimes meaning its an exercise left to the user entirely, sometimes meaning fully self-hosted and hardly local to the device being used to access the app.