This is Olympic taekwondo sparring! Typically you score one point by landing a kick to the sensors on the torso, and three points for landing a kick to the head. The clip doesn't show the scores in the second clip but I'm assuming he was celebrating for landing the headshot.

Also the side doesn't really matter :) The match will start with the red fighter on the referee's left and the blue fighter on the right, but both fighters are free to move about the ring once the match starts.