That sounds like the fans are spinning to cool down your PC. The fact that it happens when you play Diablo sounds pretty normal. If you think about it the system should heat up quite a bit after gaming so the fan running for a while is not a bad thing.
If you want to check it out, you can simply check the temp right after gaming, then shut down the pc and let the fan spin for as long as it needs to. You will see that it will eventually stop. Depending on the cooling setup you have in your case and the temperature it reaches, it may simply need more time to cool down. If you see that after like a half hour they are still spinning turn it back on and re check the temp.
Under no sircumstances can a spinning fan cause any damage to your pc, thats for sure. But manually shutting them down or turning off the auto fan control probably will!