Burning plastic sounds like an environmental hazard which is completely unaddressed in the article. At full scale, the communities near the launch site will never accept it.
There's a massive difference between HDPE (which is a hydrocarbon) and PVC (which contains chlorine and is awful to burn). Might be some plasticizers in the mix as well, but mostly they're just H, C, and O. Cl makes the real nasty stuff.
Rocket fuels can have some pretty nasty stuff in them as well, of course...
Most fuel mixes for rockets are just Kerosene and Liquid Oxygen, at least in the USA. Seems like most of the next generation are aiming for Methane and LOX.
Burning plastic incompletely would most likely produce more noxious stuff than Kerolox or Methalox engines. Maybe on par with existing Solid Rockets or Hypergolics.