Nope, it’s their server software. This is a screenshot from the Factorio webpage, which is a video game. So, the normal Linux download is the playable game and you grab the headless download, if you want to host a multiplayer server.
Your definition of “headless” is also somewhat wonky. It mostly means that it can function without a GUI, e.g. in the case of a server it does I/O via network ports and logs out any events that happen.
This does often mean that you can log off (which in particular closes the GUI session), and it continues running. But if you launch a headless program underneath your particular user, with which you’re then going to log off, then it will close regardless (and not just because your GUI terminal emulator closes).
Of course, most headless programs will have a SystemD service associated and ideally run under an isolated user anyways, so that will prevent them from being stopped when you log off.