Yes. There are two ways to accomplish this. The first option is to access each game using the left-side menu.   Select Scores and choose the particular game you're interested in receiving notifications for.  Tap the desired game, and then tap the star icon to the far right of the banner beneath the game.  The second option is to access the desired game on your Home Screen.  Once you have identified the game you wish to receive notifications for, scroll to the notifications tab.  Finally, check the box of each specific type of notification you wish to receive.