The half kneeling military press is a useful drill for learning both the alignment of shoulder hip and knee for effective overhead pressing.
There are a lot of small technique points that can go awry with the kettlebell military press. Many of these relate to what could be considered "leaks of tension" in the system. These leaks could be anywhere in the kinetic chain, from your feet to the hand holding the kettlebell.
However, some of the most common places to leak tension are around the hips and lower back, the shoulder girdle or the position of the forearm in the press.
The half kneeling military press provides effective proprioceptive feedback about the position of the hips and lower back, effectively encouraging the transmission of the forces in a straight line into the floor.
The 90º angle of one leg at the hip encourages you to more easily maintain a neutral spine position, avoiding excessive arching of the back (trying to turn the shoulder press into an incline bench press).
When you add in the two different ways of holding the kettlebell demonstrated in the video, especially the bottoms up press, you're forced to learn a better forearm position (vertical) and how to maintain even more whole body tension and alignment.
[Although, in the video, I have not used anything under my knee, it's good practice to place something soft under the knee to relieve the pressure on the knee.]