I thought it was just a synonym for "shattered", but it does seem to be more than that - there's a lot of "oak tree + lightning" in there, and not much "oops, I dropped a milk jug". Maybe it's closer to our modern "exploded"?
Here's two from 1797, both describing the same storm: "the old poor houſe was tremendously ſtruck by the lightning; the roof was entirely torn off and demoliſhed, the window frames driven in and ſhivered to pieces" and "The ship Elizabeth, retaken by the Alcmene, had her fore-top-mast shivered; as was an oak, a foot in diameter, in Yatton Church-yard."
(Do you have access to the OED via a fairly cheap route? That's something I'd really like to have).