Snap and Flatpak apps I think can do this as well, because they aren't stepping on the running binaries during the update. And you get the updated version when you relaunch.
Firefox isn't special in this regard. 100% of my applications on Windows and macOS expect to be quit before they can be updated, and is enforced either by the application, the OS, or the updater. I suspect that distro package managers don't really have a way to do an out of band update, all they can do is step all over in-use libraries and that inevitably causes the application to go a little crazy.