In my case, I had to
- Beat the tutorial
- Sit through all the fireworks and flashy flashy ('coz it’s a big accomplishment dontcha know)
- Collect assorted rewards and upgrades
- Leave the game and then force the app to quit using the Android settings
- Re-enter the game and acknowledge a new prize popup saying I had earned the WoW gift (and the Hearthstone one, big whoop)
- Enter WoW and play the game for about an hour before the gift hit my collection.