[iMore Question]

IPad Mini 4--New w/update. As in above screen shots. No reference to Touch ID in Settings, at any level. Clearly this is not an isolated problem.

[Ledsteplin]

Welcome to iMore! I saw one other case like this. Not sure what they did. But try first a hard reset.
Hold the top or side power/sleep button and the home button at the same time until the Apple logo appears, then release.
If that doesn't work, then Reset All Settings.
Reset All Settings
Go to Settings >General >Reset >Reset All Settings. This resets to default everything in Settings, including notifications, alerts, brightness, and clock settings like wake up alarms.
If that doesn't work, you may need to restore your phone as new. Not from a back up.