http://www.bloodyelbow.com/2010/4/5/1387...
Its a front kick; he is using the ball of his foot to make contact with and is curling his toes up to avoid breaking them. Its a good question and the video brings out something that I have stated before in this forum and that is sometimes changing the angle of a kick slightly to more effectively use it and this is a good example and one that I also used at times in fighting with goof success. By making the kick look somewhat like a roundhouse kick at the beginning sometimes your opponent will not bring his arms and elbows forward and closer in so soon or as much. This then leaves a wider space to sneak your angled front kick inside or in between those arms and elbows, making contact with the ball of the foot and landing your kicks to the body.
This is one of the reasons why I tell students and fighters to just not always practice throwing things straight on in an orthodox way but to instead also practice doing things like changing the angle of a kick or throwing it from an angle after positioning yourself to do so. Doing this means your opponent has to cover and protect more area than otherwise and sometimes they will think they have an area covered when they actually don't and only find that out after the kick has landed.
A low, rising round house.
Front kick hold the knee upward throughout and snaps in an upward motion at the end of the same whereas a round house turn the hip, generating its power from that joint and the accompanying weight shift.
He is using a slightly modified round house.
It is in the front kick family. The martial art I study says there are 64 different ways to do a front kick. It might be a kick he is good at and likes to utilize. And secondly an opponent that is not familiar with his strategy will get caught by his kicks. It also depends on what style of martial arts he studies. Some styles of Karate(Japan) have only a few kicks, and they are executed differently than someone say TangSooDo(Korea).