I am a pilot, I have training and some lungs-on experience with hypoxia. It is my opinion that this execution was botched; some combination of they did not sufficiently empty the atmosphere of oxygen and did not sufficiently remove CO2. The (rather shitty) article (or disorganized collections of opinions with nearly no structure and light on facts) mentions "a fitted mask" was used, which...yeah there's your problem. This probably did not provide enough isolation from the atmosphere and so he died of barely not enough oxygen.
Imagine instead walking into a classroom sized space that is full of 100% nitrogen. It's possible you wouldn't notice. In a space that large, your exhaled CO2 has enough room to diffuse away and not bother you. The fun part is, in this scenario you exhale O2 as well; breathing in this environment will kill you faster than holding your breath; being in that environment actually removes oxygen from your bloodstream. You're unconscious in less than a minute and dead in three or four. You don't struggle to breathe, nothing feels wrong, you get lightheaded, your vision narrows, the beginnings of a headache are probably your last earthly experience.
As the volume of air gets smaller, the O2 and CO2 exhaled by the condemned is more likely to be rebreathed, CO2 causes that "air is bad, need to breathe fresh air" feeling we're all familiar with, and O2 keeps you alive and conscious. One of those coffin-sized pods requires a good bit of gas flow to keep the atmosphere around the condemned's face pure.
If they put one of those medical masks they give you nitrous oxide or oxygen at the hospital with, just hooked up to a tank of N2...they probably weren't even completely excluding oxygen from the room.