However, when a company issues a stated policy of restricting law-abiding gun owners from bringing weapons into their place of business, they have effectively taken upon themselves the responsibility of keeping their customers safe.
So -- yeah, I think Cinemark is going to be sued out of existence. And rightfully so, if they do in fact have a documented policy prohibiting people from carrying weapons into their place of busines.
I will wager a rather large sum of money that the issue over which they are sued is failure to keep the perp and his weapons out, not their policy of prohibiting concealed carry by patrons.