I can think of 2 things:
1) Make sure you have downloaded the game and not just the training. Quit the game and go back to the launcher, next to the button in the left hand corner is a box that says "ELITE: DANGEROUS" above "SINGLE PLAYER COMBAT TRAINING", click on "ELITE: DANGEROUS" to highlight it and the box should change to "INSTALL".
2) I'm completely wrong about that, contact the support (link under the logo on the launcher).