I know a number of people who proudly adopt the label, none of whom had even heard of Richard Spencer before NPR and the like started talking him up. I haven't been able to find anyone who even
knows anyone who thinks it's accurate to call Richard Spencer the, or even
a, leader of the alt-right.
If anyone can fairly be said to stand in that role, it'd be Milo Yiannopoulos, so I suppose it's not entirely unreasonable that someone at NPR confused his picture for that of Spencer and stuck it on the linked transcript. On the other hand, it's not reasonable to call Yiannopoulos a white supremacist, either, so overall I'm not sure what to make of the piece, except to say that I'd think twice about taking it at face value. There is a great deal of nuance here which NPR has no reason to represent fairly, and every reason not to.