This potentially poses some difficulties for the ref and is possibly a question of game management and expectations from players.
I do agree that Marler's arm comes away and he is no longer fully bound, therefore the ball is out. If he had moved forward with everyone else he would have had to move his back foot forward, which would very clearly be "ball out". Was it managed in a consistent fashion compared to other occasions? Does this matter (technically), providing the current decision aligns with the laws?
I suspect Care was not aware that Marler's bind had changed since he was focused on the ball and the defender. I'm not convinced the ref was fully aware (in real time) that Marler's bind had changed, and decided to let play continue and the rely on the TMO to check what had happened.
How would we have managed this at grass roots, without the benefit of a TMO? Typically the ref will decide the ball is out and will call it, or the defender will ask the question, forcing the ref to say yes or no, then everyone is aware (I put this down as game management).