The position you described is used to allow the abdomen or belly to hang unsupported. Most lumbar surgery is done in this position. It keeps the pressure off the abdomen, spine, and blood vessels. The result is to reduce or prevent bleeding into the epidural space. The epidural space is between the spinal cord and the vertebra.
This position also distracts the posterior aspect of the vertebrae. This makes it easier for the surgeon to remove the disc when necessary.
There are some potential disadvantages with the prone-kneeling position. First and foremost is the fact that the hips and knees are bent. This flattens out the natural lordosis (swayback) in the low back and can lead to problems later. But preventing bleeding is a higher priority than keeping the spine in a certain position.
Scientists are experimenting with different ways to do this procedure. There’s been some discussion about straightening the hips just before inserting the metal rods that go along side the spine. Further studies are needed to look into this suggestion.