I know that P2O fuel burns cleaner due to the reduced (almost none) sulfur. Sulfur is not a greenhouse gas as your own link shows. No sulfur in that description of GHG's from the EPA.

Two separate environmental issues. Reduced sulfur is one of the reasons it is legitimate to call P2O oil a green fuel. Removal of waste plastic and reducing the amount of oil that must be removed from the ground are others. Having a process that does not add pollutants to the atmosphere is another.

P2O fuel is good stuff. Never said it wasn't. But it does not directly reduce GHG's. Indirectly, by producing oil using less energy than it would take to get the equivalent amount out of the ground, it helps.