Moving the body is the same concept. When someone kicks at a body, they are literally kicking at a target. Move the target left or right or back a few inches will cause the person to miss. Boxing is a little different because they can actually "punch into a target" versus "punching at the surface" If they punch at the surface of the then you can just move your head back a little and be safe. If they punch beyond the surface of the target then moving back a few inches won't help and that's when bobbing and weaving and taking angles come into play.
This same concept exists with kicks, but it works better, because once a person kicks they can no longer move forward. Even with the side kick that Bruce Lee uses follows this rule. When he actually kicks, his physical body is no longer moving forward beyond where he planted his foot. The other thing about it is that you don't have to be as quick to get out of the way because kicks normally travel in a consistent distance. If you can get a good estimate on the length of the leg then you can do really good with staying out of range or smothering a kick.
The difficulty with punches is that there is more than one. With kicks, you really only have to get pass that first because the second one takes longer than the first one. Even as fast as this kicks are, you'll still have time to move in or at an angle as the foot retreats. Provided that the first kick doesn't beak your structure, causing to spend your "moving time" for regaining your structure.
Front kick at 1:40 misses because the body (target) moved off center of the kick.
Front kick at 2:00 misses because the body (target) moved off center of the kick (this time because of the footwork of the sweep)
Teep at 2:38 misses because the head moved off center of Ithe kick
Side kick? at 4:08 misses because distance wasn't calculated accurately.
Front kick at 4:13 misses because he takes an angle which moves the body, and it's not a big angle, it was just enough to get out of the way. Because he didn't use a low block he still has his hand free to fire after he evades the kick. He was able to strike while the kick was still in the air.
I picked this fighter because I already knew that Yi Long likes to move in on kicks. He will either try to take an angle or smother the kick to prevent it from reaching maximum power. He comfortable with this because he understand that once the kick starts, his opponent is no longer able to retreat. He doesn't do a lot of bobbing and weaving because there are kicks involved, so the only really safe option is to move the body out of the way. Bob and weave when there is kicking and you may end up kissing a shin, foot, or knee.