I actually think the ref has a shit game. The amount of abuse he took at times was ott. I thought a lot of their players went down under hardly any contact and got free kicks and if he did book Barnes for that then, well, that's just another mistake.
Did he? Are you sure he didn't book him for kicking the player in the chest while attempting to win the ball? Either way, why? Why is booking someone wrong? It's not a case of "foul and a red or nothing".
If he deemed it a reckless challenge that is a yellow card, not a red. A red is for excessive force or denying a clear goal scoring opportunity. The booking won't have been for "stamping" or "kicking" it would have been for "unsporting behaviour". The ref, apparently, deemed it not to be a vicious attempt to stamp on the player, but an untidy challenge in which "the player has acted with complete disregard to the danger to, or consequences for, his opponent", and in accordance with the Laws of the Game has cautioned Barnes.