This passage is a really a joke. It is deliberately using a linguistic process called back-formation to create a new word from an existing one by stripping away an apparent negative prefix.
Consider the first of your bolded words: chalant. There is a standard English word, nonchalant, that is defined as "having an air of easy unconcern or indifference." However, native speakers know that non- is a common prefix of negation, so it's easy to imagine that there might exist a word, chalant, that means the opposite of nonchalant (that is, "having air of extreme concern"), even though no such word actually exists in English. (In French, there are the verbs chaloir and nonchaloir, which have opposite meanings, but only nonchaloir was adapted into an English word.)
This is true for all of your bolded words: they are English words that had what looks like a negative prefix stripped away from them, which English-speakers would understand as meaning the opposite of the original word through the logic of back-formation. However, in all cases, the "new" word either doesn't exist in English, or is extremely uncommon. Note that The New Yorker is written for a fairly educated audience, who would presumably understand and appreciate a linguistic joke like this.
Here are all of those original real words, in the same order as in the passage you quote:
nonchalant, disgruntled, disconsolate, nondescript, unkempt, disheveled, ungainly
All of them look like they have one of the negative prefixes non-, dis-, or un-.