The karate that was portrayed here is a style called "Kyokushin" and it consists of no punches to the head. Making it a sport that has intense core and thigh conditioning. It's a karate style you don't see in the Olympics, many refer to this style as the true karate (which is true)
There are a few karate styles that are like this, like Ashihara and Kudo. It's really great to see such a nice karate portrayed in a manga