What is the Alt. Right, is a popular question right now, presumably because the so-called Alt.Right is seen as having an effect on the recent U.S presidential election and to a lesser extent the rise of nationalist parties in Europe.
Commentators like Milo Yiannopoulos have tried to paint the Alt.Right as simply right leaning citizens who distrust mainstream politics, and established political parties (including the GOP) which to a certain extent that's true. Unfortunately, however, it is not the whole truth.
On the left many would describe Ben Shapiro and Yianopoulos both as prime examples of the Alt.Right, going so far as to smear them as white supremacists. Shapiro and Yiannopolous don't agree on much, but I'm sure neither would you accuse the other of harbouring views of white supremacy.
Although Shapiro does recognize the white nationalist/supremacy element in the Alt. Right that Yiannopoulos tries to downplay or ignore as to insignificant to matter.
Perhaps it is insignificant, but there many Tea Partiers, classical liberals, right-leaning libertarians and even traditional conservatives (like Shapiro) who do not wish to be associated with anything that has the tiniest whiff of white supremacy to it.
The mainstream media has been quick to jump on the white supremacy able of the Alt.Right (raise your hand if your surprised... anyone? Thought not) it plays perfectly with their narrative that Trump supporters (presumably made up of most if not all of the Alt.Right) are knuckle dragging racists, who spray pain swastikas everywhere (actually that's done mostly by the anti-Trumpers, who have made fake hate crimes their new favourite hobby.)
But the Alt.Right is hard to define because it is so broad, exactly why the term is being questioned in the first place. Sadly though the Alt.Right cannot be the new Tea party. It might, without the taint of aforementioned white supremacy, made a good catchall name for disaffected Republicans and an evolution of the tea party movement.