I mean, Spencer says a lot of things. Do you believe all of them, or only the ones you find convenient? And the same Breitbart article [1] quoted there also devotes an entire section to disposing of the three dozen or so legit would-be Nazis on the fringe.
Of course, that Breitbart article also dates from March 2016. Spencer didn't hit the big time for quite a few months after that - not, in fact, until just after the election [2], whereas "alt-right" in general had never really left the zeitgeist after its first big splash in August. But that changed when the media made Spencer its darling, because of course it did - the man is eminently hateable, which is precisely why he was made so notorious so fast.
[1] http://www.breitbart.com/tech/2016/03/29/an-establishment-co...
[2] https://trends.google.com/trends/explore?date=2015-01-01%202...
"Spencer and others have said that he created the term 'alt-right', which he considers a movement about white identity. Breitbart News described Spencer's website AlternativeRight.com as 'a center of alt-right thought.'"
This matches with what I know. White supremacy was also featured prominently in the sidebar of /r/altright before it was banned.