Yeah there is another way where you block the kick with your forearm and wrap upward trapping the leg in the crook of your elbow.
You will basically never see it in high level competition because of the risk of a powerful kicker kicking your arm off.
This one is against a front kick.
The catch shown here actually works pretty well... if you include the details you get when not learning it from a book... and when testing it in sparring with different types of martial artists.
If we start by just dealing with a rear leg, front kick... You need to get offline first, so you step with the foot that is on the side you want to go. (right foot first to go to the right) For a front kick, it does not matter which way you go... it will only change which throw you use to finish. So, you step offline, but instead of staying away as was shown, you step diagonally in, while changing levels, getting low. This gets you further offline, and gets your head out of the way of any follow up punch. By going in and getting low, I am trying to keep my left elbow (assume I went to my right, so I parry and catch with my left arm...) close to my body. If I did it right his leg should be making contact with my arm on the out side, my elbow should be just below the level of his leg. If I end up here, it is a simple thing rotate my forearm under his leg and catch the leg. We use different take downs from that point.... I won't say better than those in the video, those were done so poorly, I would want to see them done well in order to make a determination.
Whats key, is that I get offline, so that if i don't catch the kick, I still get out of the way. And I still close distance, either inside or outside. By keeping my elbows tucked to my body, I don't give up my guard, unless I get into the position I want, then I catch the leg. If not, I am in a great position, to punch. It could be a lead punch as I step in, or a reverse punch once the step lands... depends on the situation. What I like about this approach is that I stay on balance, I keep my guard, I involve head movement and a level change, and I am not left vulnerable if I don't catch the foot.
Now, I was talking about the front kick, but this works well for a round house kick as well. Only, now it matters which way you step. You have to step away from the kick, while entering. You want to put yourself in a position where his kick has to cross his own center line to make contact. That should take off a lot of the power. By moving in, you get inside the radius of where he is expecting to throw the power, which also helps. You take whats left on the upper arm, which is tight to your body, and complete the catch. (you also hope the other guy is not a Muay Thai guy, their follow through on their round kicks can still suck with this technique)
Once you have both of those variations down, you need to try to get it in live sparring, with different kinds of kickers. You won't catch every kick, but you should be able to get offline, and close distance... ending in a position where you can counter. If you did catch it... thats cool.
Some things I learned playing with this against different people... You will quickly learn that it gets way harder in live sparring, because you don't know when he will kick, what type of kick it will be or even which leg. So, I go with the percentages. (if I don't know anything about the other guy...) I always move towards the other guys lead foot. This way if he throws a lead foot front kick, rear foot front kick or rear foot round kick, I am good... same response. If he is throwing a lead foot, round kick... thats the issue. But, I am closing distance, and jamming the kick, and my guard is still in place. I still manage to close distance, even with the impact... most of the time.
The other thing I learned is that if I decide to "catch his kick" it will never happen. First I am looking for something to happen, by the time I see it, and recognize it, its too late to decide to catch it. Then the other guy knows what I am doing, and can use feints. However, if I decide to get offline of his attack and close distance, so I can grapple... many times, I will find a leg in my arms... and the times I don't I am counter punching or initiating a grappling attack.
I have caught kicks this way from MMA guys, Kick boxing guys, Kung fu guys, karate guys and Muay Thai guys. (those hurt a bit, even when you catch it) One of the Karate guys was a two time national kumite champion. Yes that is point fighting, but it means he is fast. I am not going to say that the catch is 100%... but the body movement gives me a good defense and closes the distance more often than not.