As can be seen in the video, the girl used armbar for counter the kick defense. I would like to ask if there is a tutorial of how to do it? Are there any other ways to counter the leg catch defense?
ask if there is a tutorial of how to do it
Not that I know of.
Are there any other ways to counter the leg catch defense?
I wouldn't even call the way in the video a valid way. As mattm and JohnP say, that armbar is impractical without a cooperative partner in a scripted demonstration. And not just in the "oh, it'd be so hard to pull off" - it's actually fundamentally flawed in a self defence sense, because the kicker makes themselves even more vulnerable than they need to be long before they can counter. If you watch in slow motion - or pause at the right point - you'll see that when she kicks her upper body is quite upright but at least her head is outside the reach of his jab, but after her leg is caught she actually squares up and leans in towards him while grabbing his uniform with her right hand - that means she's going out of her way to get into his punching range, and her right arm's busy and unable to move to deflect any punch he might throw. Her left arm's way out to her left for balance, and consequently useless for defending herself, and he's free to reach in and grab her shoulder, which means he could equally have punched her in the head / fight over. Practising or planning moves that involve transitioning through such total vulnerability and hoping your attacker won't do the obvious thing is suicide in a real fight. You may also observe that he's leaning his upper body forward as he attempts to throw her, rather than maintaining an upright balance and shoving her with his right arm - that's because he's anticipating and cooperating with the throw, and wants to roll safely into position for her.
So, "any other ways". If we take a figurative step back, the first problem was that the leg got grabbed. First, if you kick with proper technique and focus, they're more likely to be knocked sideways, injured, and without getting a useful hold on your leg. But, if they've read your intentions perfectly and moved sideways at just the right time to catch your kicking leg as it loses focus, then yeah - you may need to defend. Options include:
rotating your torso and hips further away from the grabber while dipping the kicking leg's knee towards the floor, while dragging the leg down and through the grabber's hold
leaning in as she does in the video, but with both arms up in front and protecting you from any punch or grab he might attempt, leaning your body weight over your trapped leg: that means his grabbing arm will be dragged downwards and his body trapped under your weight, flat-footed. You can then throw hand/arm strikes to his head: in particular, a right-arm armbar / ridge-hand strike or hook punch to the left side of his head will be very hard for him to defend against while his left arm is busy lower down holding your leg
- if you can anticipate the grab, you can be moving in ready to strike his head even as your half-hearted kick - your bait - is being caught
after your leg is trapped, bend it again and slide your kicking leg's knee across towards their back hip, leaning in with your shin across their waist: that's a standard distance-preserving position used in Thai Boxing that will stop the grabber getting close enough to pummel you; they won't have too many good options and you can pick your moment to shove them away and disengage
If you notice someone is looking to grab you but they haven't done it yet, you can:
throw in some feints such as seeming mid-section kicks that change last minute to attack the head or thigh instead, or
both Thai boxing and Kyokushin karate commonly feint a kick then throw a teep / front kick, or
there's the mawashi kubi geri (roundhouse neck kick, aka question-mark kick, Brazilian kick, ...), or
swing the knee across without extending the lower leg for them to grab, then throw some other kick (side kick, hooking kick with the heel, vertical/slapping kick "uchi mawashi geri"...) or hand technique, or
just kick really, really hard and be ready to focus the kick a bit to the side of where they are when you start the kick, so even if they slip a little sideways you'll hit full power.