It shuts down all of a sudden, right? No Windows "goodbye" screen or anything? Because that would simply be Windows Update and you wouldn't see the message because of the video's full screen mode.
Then yes, it's most probably your CPU's temperature. I see no other reason for sudden "emergency" shut down during use. Apart from maybe power variations, but that sounds sort of unlikely in your case.
I doubt there's a way to be sure. The shutdown is handled at a basic level. The OS has no say in it, right? You could dig into the BIOS, but if it's not there, I doubt it's anywhere.
I think the best you could do to be sure-ish would be to use a program that would monitor your processor's speed and warn you. "Please save your work and shut down your PC ASAP! Your processor is overheating. If it reaches 2 ° C more, the system will be shut down without any warning." Or something like that.
Every time someone I saw troubleshot / diagnosed such an issue, their only diagnostic tool was the processor's temperature. It's hot? Then that's the cause of the sudden shutdown. The usual troubleshooting procedure is to check the processor's cooling, and then, if the problem stays, look elsewhere. Sometimes, people will change the cooler without even checking the actual temperature, since it's so commonly the reason.
So, yep. If the thermal paste doesn't do, you'll have to get a new processor cooler. I doubt dust would be the problem, since it's not an old computer. Don't be afraid. They're pretty cheap. 100 $ is pretty much the highest price I saw for one (the normal ones, not the fancy ones with liquid) that was apparently "the very best, super silent and really effective".
But seriously, don't just go without looking for the issue and tell yourself just not to load the processor too much, etc. Any modern machine that overheats while just watching a video has a problem. Either the cooler is faulty, either it's not attached correctly, either the processor has an issue, either... Well, you get it. It can't be remotely normal.
In bulk, other causes, in case it's not the processor's cooling:
The cooler doesn't receive sufficient power.
The processor is faulty and overheats very easily. See what's most advantageous: buying super fancy liquid cooling to make up for it, or buying a new processor that won't overheat.
It's actually your graphics card or another component that overheats.
Somewhere in the power chain (be it the power bar, the plug in the wall, the PC's power supply or its cables), there's a problem that makes micro-cuts in power once in a while, resulting in the computer turning off abruptly.
A component is slightly misattached, and when -something- (e.g. temperature reaches a certain point, enlarging the component) happens, it moves oh so slightly, disconnecting itself from whatever it's plugged to.
You have a very nasty malicious software. Though I've never seen one like this.
