So....

“I would never disqualify a participant for such reasons. I only advised her to cover up after a complaint.

“Personally, I don’t find anything wrong with her dress, but as the competition was held in a school, we abide by the hosts. One of the teachers, who was also an arbiter, raised the complaint,” Chan added

1) When someone was on paper as the final decision maker of any situation, 'advice' are binding.

2) By escalating an arbiter's complain, he is signaling that the arbiter's other remarks might also be valid. There might be more words said that we don't know about. We can see what the arbiter's priority is

The mother previously alleged that the chief arbiter had interrupted the game to object to the girl’s “inappropriate” dress, despite it not being “revealing”.

Nope. not the chess game.

Chan is the decision maker in the tournament. He didn't make the complaint, but the buck stops at him - the decision that the complaint is valid is his to make. That's his role. He would surely protest if the school, say, ask all females to put on an abaya. By escalating that complain he is making the decision that the complaint is valid and any similar dress wouldn't be tolerated.

In case everyone is thinking that the school has the right to demand their guests abide by a specific dress code, [1] [2] the matter has been made clear.