In a hearing late in the day prior to the first game of the match, U.S. District Judge Victor Marrero was not persuaded that organizers of the $1 million, 12-game tournament had a legal right to block the websites from disclosing the moves until after each game.(7) Rejecting virtually every argument that World Chess asserted, he said, "I know this area of the law very well."
http://www.chessgames.com/perl/chess.pl?tid=88069&crosstable...
Someone else with PACER access could easily obtain the order, but from the ABC article the argument is indeed that every visitor to the site agrees to not share the move information and therefore these other chess sites must have violated said agreement to obtain the move information. Chessgames's defense is that they don't get the data from the site, but instead from watching people on Twitter (there are multiple defendants though).
This is kinda off-topic here, but this might even be technically a violation of the CFAA! Orin Kerr from Volokh Conspiracy has written about it many times, but it's not a serious possibility I guess.