I play xiv on my main monitor @1920x1200. I moved the window so only the game portion is visible, putting hte boarders off screen. It looks full screen but is windowed. Just right click the task bar icon, click "move", and use your arrow keys to get a full screen look.

Also, alt tab out of full screen, TONS of game don't support it, I crash when I do it in steam games, or damn near anything else. This is not exlcusive to ffxiv, and is likely more of a directx issue.