If you had a previous version of Final Draft on the computer, it's possible that the operating system is not allowing the installer to overwrite a locked copy of the Courier Final Draft font that's already there.
Go to Macintosh HD > Library > Fonts to see if the Courier Final Draft font is there. If it is, right-click or Control+click it and choose Get Info. At the bottom right of this information window, see if the gold padlock icon is locked. If it is, click it to unlock it (you may be asked for your Mac password again). Once this font is unlocked, try installing Final Draft again.