He wants to return to a glorified past that never existed by tearing down the current system, a return to where everyone is living off the land like early humans ("climbing the vines growing along the Sears tower"). He promotes the idea that men must return to being warriors, and something about the modern world has made them "weak." He promotes that such strength must be used to dominate, and claims it can be used to improve people's lives, as he claims with Raymond K. Hessel (whom Tyler threatens to murder if Hessel does not follow his dreams), despite the fact that Hessel is most likely left devastated with trauma and unable to move forward due to fear of being murdered. We never see Hessel's outcome, so Tyler gets to pretend he "helped" by completely traumatizing a person (reminds me of Trump bragging about "lifting people off of food stamps" when he actually kicked them off and made them more hungry, his followers don't see the outcome so they just believe the lie). Tyler captures the attention of disaffected, alienated young men and brings them under his wing to become part of their in-group, making them more likely to go along with extreme demands because now they have found family in Project Mayhem. He literally beats the living shit out of one of his men, destroying his pretty face, and yet still commands the respect of his men while disfiguring one of them potentially permanently. With Project Mayhem he intends to bring about his ideal world by force.
So we have numbers 2, 3, 5, 6, 8, 9, 10, 11, 12, and 13 of Umberto Eco's 14 features of Ur-Fascism in Tyler and Project Mayhem, in my opinion.
But sure, he's not a fascist.