I had done a little research on this a month ago or so. It is a very unique technique. I believe they refer to it as an arm lock style of putting.
Conceptually it makes sense for the way Bryson’s head works. It is a bio mechanical way of putting. The way he locks his wrists and elbows in is to eliminate excessive movement.
To me it looks like a very mechanical way to putt, and for me personally I believe it would take a lot of the feel out of the putting stroke. However, if your mind works in a very mechanical way/engineering, and you are struggling with your putting it may be worth a try.
The one thing I can say is Jack Nicklaus was considered one of the greatest putters of all time and I have never seen anyone on Tour trying to copy that putting style. Just because something works well for one person doesn’t mean it will work well for everyone.