How can I hold a chefs knife for efficiency and safety?
There are a couple ways I hold a knife.  

One, my go-to grip, is a thumbs-up grip - with my thumb braced against the back of the knife blade, and my fingers wrapped around the hilt.  Usually, I'm using my other hand curved over the blade, to move the food on either side, or add additional pressure to the knife as it cuts.  I am using the blade like an extension of my thumb, pressing down with weight behind it - and it is really good for rocking cuts.

Another grip is with my forefinger along the length of the blade - this gives a bit more precision in placing the knife, but less force behind it.  This would work for making long rocking cuts, where I need the length of the blade (it extends line of control further), or for slicing, and also for making delicate cuts, or teasing things apart with the tip of the knife.  This grip it really helps to use the other hand to give extra pressure along the back of the knife blade.

And the third, is very nearly a pinch grip - except moved back about an inch, so my grip is wrapped around the handle, not the blade.  I am pinching the handle, just behind the blade, between my thumb and the side of my forefinger, with that finger curled along the side and slanting under the handle, and my other fingers wrapped loosely around the hilt.  It's possible to edge the grip forward just a bit, so that the side of the forefinger edges into the gap where the blade falls away from the handle - but the finger is still far enough back that it can wrap under and behind the blade, and the thumb is still on the handle.  This can make a very secure grip.

The pinch grip is kind terrible, I agree with @Joe, it pulls the knife out of balance and makes the grip weak.  The difference between the width of the blade and the width of the handle weakens the grip, since the pressure has to be variable, and the majority of the index finger is kinda hanging out into space, not involved in the grip at all.  The whole thing is kinda awkward, and the videos show the thumb pointed across the blade, while to control the cut it needs to be nearly horizontal along the blade, which pulls the forefinger out of alignment unless you pinch against the side of the finger, not the pad - in which case it's more comfortable and controllable to move the grip back along the hilt to the handle.