See if this helps...
PS4: How to download games from PlayStation Store
How do I download games from my PS4 Library?
- From the home screen, go to
[Library] and select the 'Purchased' folder. - Select the game you want to download. Add-ons can be found in a sub-section within each game.
- Select ‘Download’ on the content screen.
You can check the progress of your downloads in 
[Notifications] > [Downloads].
‘Play as you Download’ is available on selected games. This function allows you to choose which part of the game you want to download and play first, while the rest of the content downloads in the background.