All competing teams, not just the winner, get to keep their intellectual property. We very much want them to set up long lasting, profitable businesses, and we know that patents and trade secrets are a big part of that. We also don't want them or us to go to jail for ITAR violations.
Of course, the winning missions will be covered on live TV, there will be documentaries, and each team is actually required to blog and post video to YouTube. But this will be done at an appropriate level to educate and inform the public without giving away trade secrets.
As an interesting aside, several X PRIZE winners (if I recall correctly, Burt Rutan and John Carmack are both in this camp, but I could be wrong) are fairly anti-patent. But that's their personal preference, not an X PRIZE imposed position.