It appears to me that the first respondant didn't understand your question, which is surprising for a site moderator. Of course I may be the one who misunderstood, so I'll attempt to restate it:
You're asking if it is possible to get your LS-XHL to back itself up to an attached USB drive without the intervention of a computer. Your confusion is over the issue that the backup software that comes with the LS-XHL is windows based.
There are two ways of looking at a backup. You might be thinking of backing up from your computer to the LS-XHL. In that case, the Windows software comes into play, as it is what drives that type of backup. In this case it makes no sense to backup from PC to LS-XHL without the intervention of a computer, since you are backing up the computer itself. For a backup from a computer to the LS drive, OF COURSE you need a computer; that's what you're backing up.
But the other type of backup is from the LS-XHL to an attached USB drive. For this type of backup, a computer is NOT required. The NAS drive may stand alone with its connected USB drive, and all computers on your network may be shut off, or even disconnected from the network. The LS will still back itself up to the USB drive.
However, for this to happen, you must set up the backup job initially. A job may be set up to run itself automatically every day, and once set up requires no intervention to keep working on its own day after day after day. But that initial setup requires that you log into the LS-XHL's web configuration interface, and that is done using a computer. So the initial setup requires a computer, and after that you can pretty much forget about it and it will keep working even if the computer is gone.
There is the issue of what happens if a backup job fails for some reason (such as a failure of the USB drive, for example). With no computer hooked up you won't be able to review the backup logs periodically to ensure the backups are occurring as you expected. However, the LinkStation drives may be configured to email you in the event of an error, and I suppose you could even have that email sent to your email-capable phone. So once again, aside from initial setup, a computer is not needed for backups to occur from the LS drive to a USB drive.