Restoring from backup does not restore some applications - I need their data badly
The actual app isn't backed up in the iOS backups, but the data for the app is backed up (unless specified not to by the developer - very rare) and a reference to the app is stored so that it can be re-downloaded from the app store. That's why you saw the "Wait" icon while it tried to download.

I would go into the App Store app and tap Updates > Purchased and triple check if you can download Photo Drag Pro from here. (The policy on whether developer-removed-from-sale apps appear in this list changes more frequently than I pay attention ;) I assume right now it won't appear, but it's worth checking.)

If that doesn't work, then your only option may be to try to pull the data for Photo Drag Pro out of the backup using a third party tool that reads iOS backup files. There are a handful of options; the one I work on is called Decipher Backup Browser https://deciphertools.com/decipher-backup-browser.html. You can use this to open and save the files from Photo Drag Pro out of the backup and onto your computer. If you need help locating the Photo Drag Pro data in the "All Files" section of DBB, there's contact links on our website and we'll help (and feel free to mention Kelly specifically if you want to make sure your email gets directly to me!)

(Note: As I mentioned, I'm a developer for the software I linked to. I want to make sure I'm up front about that!)