Yup, “don’t” was originally a contraction for “does not” as well as “do not”. “He don’t” sounds informal or “uneducated” to us now, but it used to be acceptable upper-class grammar.
It was quite common for the upper classes to use, slangy, vernacular speech in informal conversations, especially with close relatives.
Basically if you come from an established artistoicrtaic family and have the benefit of a (major) public school education then no-one’s going to question your breeding or education if you use words like ‘ain’t’, despite it’s lower class association.
I haven’t read the books or seen the TV series, but I would take the use to indcate that the speaker was close to the person they were speaking to and of perhaps of a slightly playful nature.
There’s nothing “modern” about using “doesn’t” instead of “don’t” in this case. Both forms have been used in the past, and continue to be used in the present. Which form you use depends on the grammar rules of your dialect.
I think Jessica Mitford’s books go into detail on how truly upper class people feel free to use nonstandard forms, like “don’t” and “ain’t” and “huntin’, shootin’, and fishin’.”
The Mitford involved was Nancy rather than Jessica. She’s the one who popularized the findings of Alan Ross, who coined the terms U and non-U to describe the differences between Upper class speech and speech of the “commoners.”