I watched the video (or possibly the same one at a different source?) and the tail-number was 'redacted' by a black square. A short while later, some simple research, it was aircraft 08-8199.
They have obviously managed to patch it up enough for some flight ... it flew into Ramstein just recently.
Today, it has departed Ramstein and is heading across the Atlantic at 12,000 feet.
It's not the first time this has been done ... aircraft 07-7189 over-ran the runway on landing in Afghanistan in 2012 and suffered worse damage. It was 'mostly' repaired on-site and flown back to the USA.