With its Moon announcement, did SpaceX kick off the first public-private space race?

SpaceX shocked the spaceflight community yesterday by announcing a new ambitious goal for 2018: sending two people around the Moon. The two passengers are not NASA astronauts; they are, instead, wealthy tourists, who have already put down a “significant deposit” for the trip. If SpaceX pulls this mission off, it will be the first private company to take civilians beyond Earth orbit.
The mission also mimics a possible NASA plan. A few weeks ago, the White House asked NASA to look into