Unless your pc sucks, it should have better graphics than mobile. There are no different versions of the game. The game will begin moving up on quality the first time it runs (the demo scene) and stops when your machine is too slow to play.
You can try to remove the game and reinstall it. Then see up to what level it reaches on that scene. A Samsung s4 goes up all the levels. The iPhone 5s too. And I haven't seen any pc that doesn't reach level 7.