Loading game to HDD fail

Figured I’d load both Forza 4 and Horizon to the HDD figuring I wouldn’t need the discs anymore and wouldn’t have to keep switching discs back and forth. But after doing it I still need the discs to play the game, now I have used up space on my HDD with no benefit that I can tell.

My question is, if I delete the games from HDD am I going to loose everything that I’ve earned and game progress?