For those getting this error and you've done what they recommend. I've solved this issue by following some instructions found on Reddit.

Open your Documents Folder > My Games > Open FFXIV_BOOT.cfg with Notepad (if you've never done this before you have to pick the "app" to open it) then where is says BootVersionCheckMode 0 , change the 0 to a 1 and then you must SAVE. Not save "as" just hit the save button.

Then open and try again, if it fails again, go back into it and make sure it set to 1 and didn't go back to 0.

This forced the launcher to update for me.