As has been abundantly pointed out, what is new in the MW definition is not the use of "them" to refer to singular people whose sex is not relevant, but to refer to people whose sex is not binary. The two are related but not the same. Other sources, such as the OED, have long recognized the singular use of the word. Look it up. It's the second sense of the word as defined in the OED, and yes I have a "dead tree" version before me as I write this. And if you should happen to look it up you'll find references far older than Austen. In fact I don't think Austen is cited at all, perhaps because her usage was long accepted by then. Henry Fielding is, though. The Oxford Universal Dictionary , which has long been a much shorter derivative of the once rare OED, contains the same definition as the OED. I don't know how far back it goes, but my edition is from 1933.
For those not aware of the history here, the original Oxford English Dictionary was a huge undertaking in many volumes, and prohibitively expensive until some time in, I think, the 1970's, when photocopying technology allowed it to be printed in a "fine print edition," with tiny type, fitting into two rather bulky tomes. It came in a slip case with a little drawer on top for a magnifying glass. The Book-of-the-Month Club latched onto this, and at various times offered the fine print edition as a bonus for membership.
I would note that the 1918 first edition of the MW New International Dictionary does not contain reference to a singular "they," suggesting that either the usage was less common in the United States, or that MW's then prescriptive sense of lexicography was more overbearing than that of Oxford.
Dr. Johnson is a bit ambiguous. He refers to the primary sense of "they" as plural, but then in his literary attributions uses a quotation from Shakespeare in which the usage appears to be a universal singular, using "they" to refer to "the Spaniard." Of course the interest in reading Johnson is more historical and literary than lexicographical, but it is of some interest that he threw that one in.
So, just to be clear, the singular use of "they" has long been accepted as standard English when the antecedent to which it refers is general or universal. Other literary sources than Jane Austen can be found. Austen is often cited because she used it thus fairly often, she is still read very often, and because few would suggest that her style was not literate.
Whether or not the majority of people nowadays read "literary" fiction is irrelevant to this, as is the issue of what some people call "literary" as opposed to just plain fiction.
The new usage of a singular "they" differs somewhat from the previous, accepted one, in that the non-binary connotation of the word is applied to the person described, rather than to the universality of the description.