I assume that the full NatGeo documentary goes on to explain what happened near Lake Nyos that day, but the clip I embedded above - the only one I found from NatGeo on YouTube - cuts off before an explanation.
I'll let you make a guess as to what caused all the deaths before you click through to more detailed videos after the jump.
In the above video Cody - I assume that's his name, the YouTube channel is Cody's Lab - breathes in sulfur hexafluoride, a dense, inert gas known to deepen the sound of your voice similarly to how helium raises the pitch of your voice.
Cody then immediately breathes in perfluorobutane, an even more dense gas that makes your voice even deeper.
He then comments, "wow, that's actually hard to get back out of your lungs."
And there's the danger.
Neither sulfur hexafluoride or perfluorobutane are reactive or toxic. They won't do anything themselves to your body. but they will push the air out of your lungs and make it tough for that air to get back into your lungs. The perfluorobutane, apparently, is even more effective at blocking your lungs from taking air back in because it's just that much denser than air...
Density of air - approximately 1.225 kg/m3 (source)
Density of sulfur hexafluoride - 6.17 kg/m3 (source)
Density of perfluorobutane - 11.21 kg/m3 (at 28.9oF source)
So, neither of the gases will hurt you, but they will prevent your body from getting air - which sort of includes a rather important thing to your survival, oxygen.
I'm hopeful that Cody had somebody else around to call for help just in case he didn't get air back in quickly enough.
I'm also hopeful that he didn't do that demonstration too frequently because both gases are also potent contributors to the Greenhouse effect, sulfur hexafluoride being almost 24,000 times more effective than CO2 in warming the planet (source), and perfluorobutane being 4800 times more effective than CO2 (source).
See - as the above video shows - if the oil is hot enough to burn, it's probably hot enough to boil the water you're splashing on it. If the water is hot enough to boil, then its volume will increase about 1600 times meaning that even a tiny drop of water will expand massively and push the oil above it out of the way.
If enough water drops do that, the oil splashes out of the put and will often turn into tiny liquid droplets in the air. That's called aerosolizing (like how liquid droplets come out of an aerosol can).
Those tiny oil droplets then can ALL catch fire at once, turning a tiny fire into a conflagration. (That's a big fire, donchaknow).
Let's let the Slo Mo Guys (and a few other folks) show us that happening.
Combustion - like the fire on the tiny candles - needs oxygen. Oxygen is slightly heavier than air (because air is mostly nitrogen gas, and oxygen is heavier than nitrogen), but sulfur hexafluoride is way heavier than oxygen or nitrogen or air.
So, the sulfur hexafluoride gas displaces the air, leaving no oxygen for the combustion reaction to burn.
It would be just like filling the large box with water, but you just can't see the sulfur hexafluoride.
Of course, there are problems with freely dumping sulfur hexafluoride out.