Ok, path is maybe correct.
But are you sure you didn't rewrite frontend translation file by that one from backend?
I checked both versions (1.5.7 and 2.0) and frontend ini file always starts with this code:
; @version $Id$
; @package ARTIO Booking
; @copyright Copyright (C) 2010 ARTIO s.r.o.. All rights reserved.
; @author ARTIO s.r.o., http://www.artio.net
; @license GNU/GPL http://www.gnu.org/copyleft/gpl.html
; @link http://www.artio.net Official website
COMPULSORY ITEMS="Compulsory items"
; Date formats
DATE_FORMAT_LC2="%d %B %Y %H:%M"
DATE_FORMAT_LC3="%d %B %Y"
DATE_FORMAT_LC5="%a %d %b %Y"
DATE_FORMAT_LC6="%d %b"
But this part is not included in your example. When I check your file, it looks completely like admin ini file.