
People don't want to understand the context of the sport. This is like calling an indirect free kick (without any warning) in a Champions League final on the goalkeeper for holding it longer than 6 seconds. You can try to point to FIFA's Laws of the Game, but you'd look silly to everyone that knows soccer because of the open-endedness of the rule, unclear interpretation and the stakes of the game. Just...don't do it.
What the coach actually admitted to was making gestures, the actual rule governing 'coaching' means Serena would have to been aware and receiving communication. Making hand gestures isn't enough; if he was behind a pillar or in the stadium bar it wouldn't matter. The coach also said he didn't think Serena even saw his gesture, and it happens all the time. Nadal's coach does it, Federer's, etc. They showed a split screen of it in real time and Serena wasn't even looking in his direction for majority of the time and even if she did, to be certain she even knew what was happening form the fat end of the court is a stretch.
Bottom line is, let it go. Refs shouldn't be stars in the middle of matches in any sport, especially important ones w/ vague not not oft-enforced rules. To not understand the role of the umpire in this is because people who don't watch the sport are adopting hot takes (more interested in the 'HURRR SEXISM' or 'HURRR GENDER CARD' debate).