This is very easily explained.
Richard Spencer wrote for The American Conservative, then Takimag, then started AlternativeRight.com. He was basically a race-aware libertarian. A lot of early Ron Paul supporters were, the Lew Rockwell types.
If you were a libertarian or conservative activist type during the Bush or Obama years, you might see him at some reception or something, along with various other aspiring politico types.
Then he started the H.L. Mencken Club. Again, mostly edgy libertarian types and paleos. It still exists, still does stuff. The main thing everyone was against was the Iraq War. Those are the types of people who appeared on RT (remember that show Adam vs. The Man?)
Richard Spencer became more devoted to race and gradually became more marginalized in the established political circles. But then you had the grassroots rebellion against amnesty, and then Trump. And you had a political force that was, generally, anti-war, anti-immigration, anti-Bush era conservatism.
An "Alternative Right" if you will.
Gee, who started a site with that name? And who had been writing and speaking about these things?
So the media, being the media, looked for a kind of spokesperson for these ideas. Richard Spencer, being Richard Spencer, decided he could be that person. And so the media said he was the "leader" of the Alt Right.
Of course, there's no real "leader." But Spencer didn't come out of nowhere, he's not some Russian spy, nor is he CIA, nor is he even implausible as a spokesman. He's a guy who, because he started a website with the right name and spoke about a lot of relevant ideas in the years before Trump, suddenly became relevant when Trump ran for office and neoconservatism was seen to be discredited.
Recent events have made him less relevant. But now, with Syria, I think the people who call themselves Alt Right will be relevant again because they're against the war and willing to oppose Trump.