"Gutter oil", digou you is any illegally recycled and refined oil. It's not necessarily from actual gutters: the "gutter" can be figurative. To be clear, does include, rarely and in the most egregious cases, literal sewer skimmings, but is also buying used cooking oil from food vendors (like from deep fat fryers and grill traps) and animal carcass rendering. Then refining and selling that oil for food use rather than as biofuel or other industrial uses. It can even apply simply to just using once-virgin frying oil for longer than regulations allow.
It doesn’t seem to be common, but there seem to have been some scandals around that, and an increase in regulations. Really gross!
It's more common to unsafely reuse oil than pull it from the sewer. This is done everywhere to some extent (bad grease at a fast food joints, etc), but China does it on a bigger scale.
How do people ever consume that without immediately getting sick?
I think people here are confusing "cook with" to mean either "the fuel source to cook" or "the oil in the pan to aid in cooking".
Unfortunately, no. See also, "frying with transformer oil".