The definition given above, from 1913, is circular. An intoxicant is that which intoxicates. If you follow that to intoxicating and then to intoxication, it will describe it as "the act of intoxiating". This inability to find a precise definition is not just a result of the lack of sophistication at the beginning of the 20th century. It is, indeed, difficult to find a definition of intoxicants/intoxicated.
Intoxicants are a subset of psychoactive substances, which are substances that produce some change in any of these categories: mood, perception, cognition, physical reflexes or behavior. The problem arises because not every substance that is psychoactive produces intoxication. The defining characteristic of what makes something an intoxicant is hard to describe.
Caffeine and nicotine are both psychoactive, but generally are not regarded as intoxicants. For a long time, those were really the only two common drugs that people would encounter that were in that category, as well as perhaps NSAIDs such as ibuprofen. But in the year 2019, there are a wide assortment of supplements, herbs and prescription drugs that are psychoactive, but not intoxicants. Kava kava, melatonin, valerian, St. Johns Wort, kombucha, "smart drugs" such as piracetam, gabapentin, fluoxetine, bupropion...there are a wide variety of substances that produce changes in mood, perception and cognition, that we wouldn't call intoxicants.
So what makes an intoxicant? My own answer, to paraphrase a supreme court justice is, you know it when you feel it.