A significant part of Depp's case relied on the argument that he was "only" violent to Amber in response to her behaviour. He admitted being violent to her. His claim was that it wasn't his fault and therefore he should not have been described as a wife beater. The judge not only disbelieved Depp's account of the relationship, he also found that regardless of whether or not Amber provoked him or behaved badly, he was violent towards her and that therefore the "wife beater" epithet was not libellous.
Sure, if this came before a criminal court with a jury they might find differently, although given Depp admitted violence it may well not end up in trial. And to dismiss the decision of a senior High Court judge who made very clear factual findings on the balance of probability is really clutching at straws.