There is a reason behind every action a person takes, whether conscious or subconscious, that has led them to that exact point.
The most important question in the entire universe that I have ever learned to repeatedly ask myself is: "Why?" If you can understand the rationale behind why somebody acts a certain way or make a certain decision, that can lead you to better understanding the situation.
This is true in Magic, of course - asking yourself "Why?" after every single play can yield great dividends. Did you ever stop to think what it meant that they played Llanowar Wastes into Thoughtseize on the first turn? By asking yourself the question, "Why?" it becomes apparent that means their hand doesn’t contain any basic swamps, which could prove important a few turns down the road when you’re wondering if you should play around Bile Blight or not and they haven’t played a second black source yet.
But this is also true in all of life. It is, in fact, one of the greatest things Magic ever taught me. And in a situation like this, I would ask myself: "Why?"
Now, I wasn’t there. I can’t exactly see the situation. But if I see somebody ripping up their cards because they lost, I ask myself that question. And the answer I come up with is that they feel something is wrong and are either sad or angry about it. And, perhaps more importantly, that I can try to help.
I think it’s important here to not see this as a threat toward you, but as somebody who is deeply distressed. If I was in a situation like this, I’d kindly ask if everything was alright.
It’s possible the answer is silence, or a “No, screw you.” In which case, it would be best to back away. Perhaps mention it to the TO and see if he can help. Many people probably don’t want help from the person who just defeated them, and so the TO might have better fortune than you.
However, it’s also equally possible that he might express to you a crucial sentiment and that you could turn his day around. “Look, I’ve just had a really bad day.” At which point you can talk about it and try to help them. You help unravel the "Why?"
Maybe they tell you that “My girlfriend broke up with me and I’m really mad” or “I don’t know why I even bother living anymore.” There are real actionable things there that you can help with, or at least talk to your organizer about helping to turn their day around
Always remember that you can’t control other people’s actions. You can influence them, you can talk with them, but you ultimately can’t choose them. At the end of the day, you can’t decide how this person acts. But you can certainly go in, putting your best foot forward. Maybe you don’t make a difference, maybe you do - but at least you know you tried and can try and point the TO toward them with more information about the situation.
Worst case, you get stonewalled and they glare at you. Now, that’s not fun. But best case, you save someone’s life. And that’s a trade I’ll make every time.