Indeed, Peterson's libertarian propaganda would contradict his manly social Darwinism. On the one hand, he'd whitewash capitalism by pretending the competitions are fair or that we all have a say, which makes the results of capitalism better than any attempt at central planning.
On the other, he'd concede that our societies are riddled with dominance hierarchies, which amount to another form of central planning. In short, Peterson would have to prefer the private sector's central planning (the dominant voice of the top one percent), to that of the public sector (the government).