I'm pretty sure the game assumes very acute alcohol poisoning, the kind that might prevent breathing altogether--which I'm not even sure is something that's going to realistically happen, due to general lack of coordination causing loss of ability to drink further or vomiting causing loss of further drinks or similar or, hell, as mentioned above, aspiration causing death first, but the game simulates none of that, so just losing lung function completely is the way that goes.
And all of that assumes nobody is around to help keep the drinker from killing theirself with acute alcohol poisoning, which is a reasonable assumption in real life but not in Dwarf Fortress due to the total lack of behavior coded in for that kind of thing.
It's also worth noting due to dwarven drinking and sleeping habits: they usually die currently either due to a tavern keeper present shoving cups down their gullet or barrels littering on the floor that they will gladly kegstand. This means, when they choke on their vomit or otherwise ceasing breathing, they are very often surrounded by at least 10 dwarves due to tavern populousness.
The threshold is also extremely steep, but another thing that bothered me is how the dose of alcohol ingame feels less like all beverages are halfway to hard liquor, rather than being the low alcohol content you'd see actually filling barrels and used to actually hydrate people with.
One short-term solution, i'd imagine, is to make unconsciousness onset a little earlier, make suffocation onset a lot later. Aside from that, I imagine testing needs to be done to make extra sure that tavern keepers won't force alcohol into an unconscious dwarf (I have my suspicions, but no evidence).
One thing that would be cool in the future is a tantrum variant that involves a dwarf stealing a whole barrel of alcohol and liquor and hiding in their room/a small room/stockpile/barracks. From that point, they'll nurse off the barrel until the tantrum ends they run out of alcohol, or die from alcohol poisoning due to a combination of poor disease resistance, some willpower or focus (to resist the unconsciousness with, if applicable at this point), and high indulgence rating.
Speaking of which, for situations like this, tantrums, or for any other reasons, a way to designate a fort member or visitor for arrest for arbitrary, good, or made up reasons should be in order.