It makes little sense to use a carabiner as illustrated in the video, as explained in existing answers.
It may occasionally make some sense to hold and use one in another way: placing it in your palm and wrapping the fingers and thumbs over it, such that the "fat end" projects slightly from the little-finger side of the palm. This will give you a steel striking surface, and the rest of the carabiner will rest against a large surface area of relatively fleshy palm and fingers, spreading the impact to your own hand and minimising the risk of damage. The grip would be largely similar to using the base of a torch or keyholder:
(image copied to illustrate the kind of grip I describe above, turned up by a google image search from a website titled "Gentleman Warrior Self Defense System Volume 3, Kubotan" that I otherwise have no connection with or knowledge of).
(If you instead have the smaller end projecting, you'll get more localised pressure for the strike, but may have more localised pressure inside your own hand: you'll be supporting all the force of the strike along the far, fat edge of the carabiner where your thumb is, rather than all around the sides.)
Having that hard surface to strike with - hammerfist style - may help a weaker person inflict significant damage on a stronger person - evening things up a bit. A strike to sensitive targets such as the nose, teeth, temple, knee-cap or collar bone may be made more effective. I'd only suggest considering it (or more generally, grabbing anything similar to fight with) if you felt you otherwise weren't able to defend yourself, felt this might tip the balance in your favour (and not just make the other person angrier and more vindictive), and the fight itself was unavoidable.
Hammerfist style strikes are often easy to block though - your striking arm can be easily grabbed, so this will work best with the benefit of surprise, when dark, or when combined with a feint or combination attack. Once you strike and they're aware of the carabiner, if they're still a threat and you still can't run/escape, then you'd want to get as many follow up strikes in as fast as possible before they can adjust their defensive tactics. If your arm does get caught and they're much stronger, and you don't know "escapes" to twist your arm out of their hold, then instead of struggling uselessly - hit quickly with a still-free limb (palm, elbow, knee, foot) to another vulnerable target and hopefully they'll let go of the hand they've grabbed.
A skillfull but weaker person could also use the carabiner to inflict damage whilst blocking - striking shins or instep or the ulner or radius bones in the forearm, or even at the wrist. An untrained person has neglegible chance of lining up their hand with a particular point in the attacking limb and blocking effectively.
All that said, if you're planning to explore this, do follow Steve's advice and try hitting a punching bag or similar target that way - gently at first - so you can learn the best grip and whether it'll hurt your hand. Further, JJC8008 has a good point, and you should be prepared to pocket, drop or throw the carabiner at some stage during a fight if it becomes a net liability and you need to grab something / wrestle etc..