Reinforcing a shelf supported only by pins
Cleats.

Well, If I didn't simply add up what this expletive redacted liquor cabinet just cost me (not counting husky-containment and mopping time) and shoot it into the sun to be wholly replaced with a decently made hunk of furniture, which I'd be fairly inclined to do after what you just went through. 

I would glue and screw 1x2 wooden cleats (non-adjustable) to the sidewalls where you want the shelves to be. Depending how flimsy the shelves themselves are, I might also put a couple long 1x2 on the bottom of each shelf for reinforcement. 

Alternatively, look for an adjustable steel wire rack shelf unit that fits in the cabinet - there being doors, you don't have to look at it except when getting bottles out. 

On the positive side, at least the marble-topped table wasn't a fishtank ;-)