Does the Power Nap support the purchased apps download?
I think the key to when/how App Store downloads are process is, according to the link you provided,


  Mac App Store downloads are checked once a week.


You didn't give it enough time.

The way power nap works is that "Sleep" takes priority.  If you want to put your MB to sleep now for whatever reason (say, you are going into a meeting), it doesn't make sense for your MB to say "no, I think I will continue downloading"  

There is a "schedule" or a time interval when your MB will wake.  Once per hour to do something small like check mail or your calendar.  Once per day for updates (bigger activity) and once per week for pending downloads.  

To check for these things, it has to come out of sleep "half way" - meaning enough to turn on networking and your drive, but not enough to bring up your full GUI and related services.  If your MB is going to be checking and downloading continually as opposed to the schedule, then it's not going to sleep; which defeats the purpose of putting it to sleep.