This is a safer alternative to the regular military press because it engages the serratus more easily, which helps stabilize the shoulder joint. It's also easier to keep the delts under constant tension during a scrape the rack set.
You'll notice a much better pump in the shoulders than you would with a regular military press. I've seen a lot of people with shoulder issues be able to do the scrape the rack shoulder press but they were incapable of doing a military press.
You can lean forward at the top of the movement. (Look at what Nick is doing when the bar is overhead.) This is a great way to work on shoulder mobility and constitutes a form of loaded stretching.