//Of course you might argue that a non-striking batter starting to run before the ball is delivered is equally illegal,...//
Why would you argue? It's not illegal but the non-striker is liable to be run out. Law 41.16.1:
"If the non-striker is out of his/her ground at any time from the moment the ball comes into play until the instant when the bowler would normally have been expected to release the ball, the non-striker is liable to be Run out."
But that, of course, applies to cricket. I don't know whether the same applies to the game that was played this afternoon.