I believe the framing is something like buying locally on armslist.com, where the buyer and seller agree to meet up face-to-face to make the sale. No mailing it.
Reading the article and a few others, this new regulation seems like election year posturing that doesn’t actually change much for the average person. The regulation is expanding who must register as an FFL from “making their livelihood from gun sales” to selling guns “predominantly to derive a profit”. Whatever that means. But it seems like it is specifically meant to exclude the occasional sale by a private person, which means that a private person happening to sell a gun at/near a gunshow or through armslist seems like they are still in the clear.
Where that line is will surely be hashed out in court, but it seems like the simple sale of a single gun from one person to another is unaffected.