In "The Small Room," what alcohol were they drinking?

In "The Small Room," the most commonly referenced alcohol is the martini. A martini is a cocktail made from gin and vermouth. This choice serves two purposes in the story.
First, martinis are strong. Depending on the gin and the exact mixture, martinis will hover at around 30% alcohol by volume. For reference, wines are usually 10–15% alcohol by volume, and beers are usually in the 4–8% range. Sarton emphasizes this with references to "post-martini exhaustion" and "the dangerous martini-induced operation of memory."
Second, but related, is the martini's association with indulgence and alcoholism. The phrase "three-martini lunch" has entered the American vocabulary to refer to professionals with the time, and fortitude, to indulge heavily in alcohol during the workday. 
One last note: the most common garnish in a martini is a single green olive. Olive Hunt's name is a nod to this fact.