I think the broader point is that the 'free speech' sites that these guys make end up being overrun by the alt-right and the out-and-out fash.
But, on the question of Peterson being alt-right, his arguments for a willful re-adoption of mythical 'archetypes' as a basis for modern society is... well, excatly what happens with all far right ideologies, where a conception of social order is influenced by lobsters. (Cherry-picking bits of animal behaviour to explain human society is a mug's game, but if we were going to go down this route, why not create some vision of frozen gay ice cream orgies and child rearing, based on penguins?)
But the real smelly herring in Peterson's schtick is his conflation of Marxism, post-moderism, and general identity politics. It's an invented bogeyman, detached from any real analysis of the cornerstones of modern poltiics. Again, it's absolutely a key strain of any rightish movement.
A lot of this could be explained as him being more of a grifter than anything, but ¯\_(ツ)_/¯
Not that I agree with him, but in Peterson's defense he talks about lobsters just to show how fundamental the mechanisms related to hierarchies are in animals (point being they have existed for hundreds of millions of years, so they must be really important). You can't say the same about the behavior of penguins.
