Playing while downloading game in the PS4

Solution 1:

This behaviour is completely possible. According to the Features page of playstation.com:

Play as You Download

Increase your play time with the ability to play games while they’re downloading titles. When a player purchases a game that is enabled with this feature, the PS4™ system downloads a portion of the game, so play can start, while the rest is downloaded in the background during actual gameplay.

When a certain part of the game is downloaded, you can play. You can only play a certain part of the game, as pointed out by Nitro.de. In case of DA:Inquisition you can only play until the Tutorial Boss. You are more likely to hit the limit when your download is slow.