To expand on this: the fundamental problem with all stoves is the need to drive the fuel up from the bottle and into the burner vents where it can be burned. The problem in that on its own fuel often does not want to do that, especially when it is cold. How exactly they accomplished this in the past is actually pretty tricky to pull off, so it's not surprising that he expired while trying and failing to light his stove.
Your typical modern pocket stove[0] operates on what we call "Isopro" fuel. It's a mixture of isobutane and propane that's really excited to return to a gaseous form. The stove sits on top of the bottle, depresses the valve built into the cylinder, and regulates the gas leaving on its own. They're convenient and easy to operate, but they were invented well after 1908, so they weren't available to him. Also, while modern fuel mixes are proudly marked as "all weather", they are not. Depending on isopro fuel in freezing temperatures will at best leave you with canisters that perform poorly, at worst they will leave you without any fuel at all. These are not recommended for winter camping.
Liquid fuel stoves[1] need some mechanical pressure to get the fuel to the nozzle (since liquids tend to stay down) and some starting heat to convince them to vaporize to a gas for easier burning. All liquid fuels include both some sort of mechanical pump, usually on the fuel bottle, and a design that allows the fuel line to get hot enough to vaporize it. Modern liquid stoves often run the fuel line through the flame, which can help even run isopro fuel at much lower temperatures. The starting procedures[2][3] for all of these stoves involve burning something, usually some of the fuel for modern stoves, in a small "priming cup" below the main stove. This early burn pre-heats all of the stove, which allows it to begin vaporizing the liquid fuel even in the worst conditions possible.
The issue, I think, is that kerosene is a pretty inconsistent fuel, and not one that plays nice at lower temperatures. Kerosene has a surprisingly high freezing temperature of -47F, and is probably a real bear to light at sub-zero temps. I suspect that's why it's recommended that you use alcohol to start the fire, as alcohol freezes at about -173F. And that's assuming that by "petroleum" they meant kerosene. Gasoline or Diesel might start misbehaving at sub zero temps too, and fail to light with a match alone. Perhaps a mix of "petroleum" along with other unpleasant substances could have been enough to light the stove, but it appears to have been too much for the already exhausted explorer.
[0] - https://www.msrgear.com/stoves/canister-stoves/pocketrocket-...
[1] - https://www.msrgear.com/stoves/liquid-fuel-stoves/whisperlit...