It's a somewhat suffocating passage in that it suffocates logic.

The way I read it is that the Dundee and Glasgow men drink for fifteen hours--and that they pass out at the same instant, but that they are non-the-worse for having done so. Drinking for so long would kill a normal mortal--at least drinking this strong drink of which they are capable drinking. But not this man from Dundee and the one from Glasgow.

So, I'd choose the second set of definitions since neither man literally died, but, instead, passed out or was extinguised, to speak figuratively. I find it a clever use of the verb to suffocate since liquid, as might be expected, was the extinguishing (second definition of suffocate) agent. And I suppose the fire that was being extinguished was the desire for alcohol!