It is a combat grip style, that they used to teach at the FBI Academy, that predates the currently in vogue both thumbs forward grip. The shooter in the picture has the left hand a bit too far forward. The theory is to lock the left thumb onto the right wrist, with the left index finger in the groove formed by the middle and ring fingers of the right hand, middle finger in the groove below, and the ring and little finger cupping the bottom of the grip from below.
The left thumb actually ends up lower than you think, and I've never seen anyone get bit using this style of grip. There are quite a few highly accurate older shooters who still use it. I cut my teeth on wheel guns, and it works really well when firing single action. You might want to try it and see if it works for you.