Multiple devices on a single Google account - App/Setting Syncing
No, there is no built-in way to sync apps between devices. Google Play backups are generally only accessed when restoring apps onto a new device (or one that was factory reset).

If you have root on the devices, you can manually sync app data. You could copy the data folder for each app manually. Or you could use Titanium Backup or any other backup app to do it for you. 

With the paid version of Titanium Backup, you can back up and restore from Google Drive or Dropbox, so it can be done wirelessly. And you can set up schedules to automatically backup certain apps. Restoring on the other devices would still be a manual process, though.

Essentially, if the specific app developer didn't create a built-in way to sync itself across other devices, you'll have to do some tedious manual work to shuffle data around.