What does the iPad Mini warranty actually cover? I am grasping at the straws here...  I am trying to read the iPad Mini US warranty, but I can't make heads or tails out of it.

Does it cover accidental damage?

Here is what happened.  I got my kid an iPad Mini 2 weeks ago.  At his mom's place, he placed it on the table, his mom was cleaning and put it on a fold out bed where his grandma stays when she comes there.  

The grandma, who can't see very well, then folded the bed and bent the iPad mini.  It's still kind of functional (in that it beeped, when we tried to locate it via Find My Phone app), but there is a bent and the screen is cracked.

I seriously want to scream, still, 2 days later, but...on an off chance, does the warranty cover accidental damage?
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.