Texas Roadhouse should have it's lawyers go after that website that is spreading defamation, lies about them closing. Attorneys will make sure that the website shuts down, all compensatory damages are paid and even criminal charges are filed. They are spreading lies on purpose and they should be held responsible for it.
From the legal perspective, this is a clear cut and I do not think this even needs to go to a lengthy trial with armies of legal personnel involved - that company would fold quickly and they would pay legal damages ASAP - Texas Roadhouse would win in no time.