No, the article you linked says “The Third Position is a set of neo-fascist political ideologies”. It does not say that fascism in general is neither left or right. I’m not talking about the word “fascist” used as an insult.

Since you linked to another Wikipedia article, you should know that Wikipedia defines fascism as far-right:

Fascism is a far-right, authoritarian, ultranationalist political ideology and movement, characterized by a dictatorial leader, centralized autocracy, militarism, forcible suppression of opposition, belief in a natural social hierarchy, subordination of individual interests for the perceived good of the nation or race, and strong regimentation of society and the economy.