This was not, to my understanding, connected to the X Prize. Also they didn't win the X Prize according this article [0].
[0] > A team led by Burt Rutan would [claim the X Prize eight years later](https://arstechnica.com/uncategorized/2004/06/3908-2/), barely within the deadline. Rutan’s team built SpaceShipOne, a small rocket-powered vehicle dropped from an aircraft.