I can think of a few ways to answer that question.

One is whether or not the material can be re-consumed or otherwise recycled and isolated from broader ecosystem damage by non human-designed biological or physical processes. Petroleum derived plastics don't fit that definition (yes I know that every few years there is a "breakthrough" plastic-eating microbe engineered or discovered, but it hasn't really dealt with the scale of the current problem). Curiously CO2 is "natural" by this definition (plants consume it), but unfortunately not anywhere near the rate needed to remove how much of it humans put into the atmosphere.

The other is that consumed material is "natural" if there is a near-term counter process, either pre-existent or emergent, that will shut down the "natural" process. For example, overgrazing by wild ruminant herds in an area will result in a population explosion, which will eventually result in population reduction either via starvation or predation. We know that the overgrazing by wild ruminants is a "natural" occurrence because the ecosystem has evolved counter measures. In the case of humans burning petroleum, there is no natural counter-measure.

Then again, perhaps climate-change and the resulting social upheavals will be exactly that. It's too early to know whether humans are going to be able to dodge the impact of that, or if climate change is to us as the disappearing pasture is to the wild ruminants.

"non-feedstock energy [for plastic production is] (between 1.4 x 1018 J and 2.2 x 1018 J)". Non-feedstock means the stuff that doesn't turn into plastic, but just powers the product. From the same paper, adding both feedstock and non-feedstock together:

"between 2.5% and 4.0% of total U.S. primary energy consumption in 2008 was due to the energy for plastic."

Also, plastics are a fossil fuel, and a lot of waste plastic is burned for energy production, which results in significant fossil-fuel based CO2 emissions.