First off, there are a *LOT* of subtly different ways that you could hold the sticks like this, and most of them aren't good for much but carry increased risk for injury. If you wanted to play very lightly with finger technique, then this grip could work fine, but... what does it give you that French Grip or American Grip doesn't already do better.
It reduces the angle of the sticks to the forearm to about 50 degrees, but on the drum set, a bigger angle is advantageous because it allows better mobility around the kit and more power.(To reduce the angle to 0 (parallel) then you'd have to hold the sticks between the pinky and ring fingers). Speaking of mobility, I see it as reduced in general with this grip because of that angle and also because the thumb isn't available to manipulate the stick much.
Reducing that angle doesn't allow for better Moeller strokes, as the angle actually allows for more power. But if you want better Moeller strokes, than you want to put the fulcrum closer to the line of the ulna. Here the best is pinky grip. That grip puts the fulcrum right along the axis of rotation and allows for much better energy transfer (read louder and faster for less effort). The reduced power in The Claw grip is great for playing quietly, but again don't you already have that in French? C
I wouldn't go so far as to say it is wrong. It is a workable technique - especially with thinner drum sticks that reduce friction on the skin between the fingers. armine Appice seems to have developed his way of using it - but like he says, for real drumming he switches to the common ways of playing because they work better.
A friend of mine, Kevin Foley, who used to play for the extreme metal band Benighted showed me this grip that he'd use on blast beats (check it out in action here). At the time, I had just got back into drumming after a 4 year hiatus, and though I used to play a lot of metal before, extreme metal was brand new to me (and probably a bad idea to jump right into right after a big break from the kit), but I found it quite helpful in that setting, although the blisters were crazy. I still use "the claw" when I play sometimes - mostly to give my thumb a rest if I hadn't had time to warm up properly and I'm cramping.