When Kushner updated his security clearance forms, the information became kinda-sorta public in that I believe credentialed journalists have access to such public documents. But simply knowing there was a meeting did not give them access to the e-mail chain. Unless those emails had been turned over to the FBI, Mueller, or one of the congressional committees investigating Russia in response to subpoenas for "all relevant documents, etc., then the only people who knew about them were inside the White House.
Aides and Staffers of various WH warring "factions" would have known about them, either by being involved in cataloging, scheduling or being in briefings (or earshot, for that matter) as the meeting was being discussed. I personally believe that someone in the WH leaked this story to NYT, forcing Don Jr. to "out" himself. My top choices? Bannon or Kushner.
It could have been Goldstone, but a low-level Russian lacky like him would never have leaked those emails without strict instructions to do so from the top of the Russian food chain, and I personally fail to see what benefit Putin has gotten out of this.
