In my experience (lawyer in Palo Alto for 7 years), parties can agree by contract to do or not do many many things. Even provisions that limit legal recourse, like the much-decried mandatory arbitration clauses [1] have held up all the way to the US Supreme Court. I would be very interested to know what legal basis there would be to invalidate a license agreement that says: you can have access to this content but only if you promise not to tell other people about it.
1: http://www.nytimes.com/2015/11/01/business/dealbook/arbitrat...
And "there are no limits to the content of contracts people freely enter" is obviously an untenable position – we'd all agree that a provision giving me your kidneys, hidden somewhere deep in the ToS is unenforceable.
I would imagine that the websites that give play-by-play info may have paid for the right to publish information about the game, or they may be able to just watch it on TV (or live) and update their info that way. As another commenter noted, the organizers could have set up the competition to forbid the audience from disseminating info, but they didn't for whatever reason.