This is going to address your previous post as well.
The reason you don't see Machida teaching the grabbing aspects of karate (hikite) is because the average MMA combatant is too fast and too strong to commit yourself to them in that way. When you grab your opponent, you have gained some control over him but you have also tied yourself to him. You are in his striking/clinching range and most guys in MMA can take advantage of that. It's also why you don't see alot of Wing Chun in MMA, at that range you are easy to hit and if you can't fight at any other range then you have to constantly place yourself in danger to be effective...and that's bad.
Turning to the image. I don't want to get into a side conversation about the shortcomings of kata but what you see is a stylized version of the same technique from the Krav Maga video. The man in glasses has simultaneously blocked a strike while stepping in and striking. The only difference is that the karate-ka has decided to control the opponent's arm rather than circle off, like in the video you posted.
As far as whether your fist is vertical or horizontal at trapping range, I can't speak to that but a solid hook to the body can be thrown at that range with a vertical fist.
To go one step further. You seem focused on how exact one technique is visually to another. As any fighter will tell you, picture perfect technique is rarely achieved in the heat of combat. What matters most is the principles dictating your choice of technique. Two boxers might throw visually different jabs while using those jabs for the same purpose.
It's why I don't get these style arguments. The principles of a style are what determines its effectiveness. Those principles will dictate the techniques they teach and how they are to be applied. A great fighter masters many principles of fighting then adds the techniques that allow him to best demonstrate those principles.
Don't worry I know I owe you a video.
Edit: I see you added a statement about bursting. Bursting is just rapidly closing the distance, every martial art, from boxing to wrestling and everything in between, teaches that. The more important thing to remember is that you first learn the mechanics of a technique then you learnhow to apply it in a fight. The man in the image is demonstrating the end stage mechanics of what the Krav video just threw at you.
What I saw in the HW video was a block that resembled karate, but is also in WC, and an unmistakeable WC punch. That strike is unique to WC. And if another martial art has it, it was added later and is now a modernized mixed martial art, just like Krav is.