Well, a stand-alone chapel still needs to be consecrated, if it is Catholic. I read on this thread that this "chapel" has a "congregation" of 70. Sounds like some kind of independent Catholic group, to me.
Whether or not one likes Mahoney, he is still the ordinary for Los Angeles. If Gibson built this chapel outside of his approval, then it's likely SSPX or even SSPV (though I can't imagine him submitting his movie to the Vatican if he thought the chair of Peter was unoccupied.)