What does the iPad Mini warranty actually cover?

No - damage caused by external forces is excluded from all Apple Warranties.

It lists some other hazards that don't get covered as a manufacturing defect like fire, liquid, earthquake, etc.

AppleCare plus does however cover accidental damage of all sorts as long as you have the device to hand in. (It doesn't cover loss).

Many people have some coverage from a credit card or other insurance - so you might check that and depending on whether you are pre / post purchase (or within the time widow when you can buy AppleCare for that iPad) to see what your best options are for coverage.

In your case - you might get it to Apple as soon as possible - just because the wording is to deny coverage - sometimes there are times when an exception could be made or some compromise reached - especially when the device is very, very new and you were unaware of the AppleCare plus when this was gifted / purchased.