I don't know of a gamified version (but would love to see one), but for help identifying, validating, and tracking sightings you may find the Merlin app from TheCornellLab useful.
Oh, I definitely use and love the major apps. I was thinking more in terms of repetition and reward to aid memorization.
There are numerous birds i can identity by sight or sound rather easily, but... I still struggle with mixing many smaller finch sized birds; females and juveniles against similar colored males of another species; and how numerous calls sound very alike.
Having an app to drill and test me would be wonderful.