You can make plastics out of natural gas , and there's a shift to that happening. Also for some plastics some companies are starting to use biotech. And as for drugs, there are alternative routes to oil , at least at the research level - but it's a far easier problem, since it's less cost sensitive(per volume).
Distinguishing NGL from petroleum is fairly disengenuous, and it's one of several games that's played with NGL reporting in US fossil fuels reporting. They're treated as oil where convenient to do so, as not oil otherwise (much of the touted increase in US domestic "oil" extraction in recent years has been NGL, where it's treated as "oil", but here for plastics, EIA treat them as "not oil").
No, NGL isn't the fraction of crude oil that's synthesised into motor fuels such as gasoline, kersone (jet fuel), or diesel. But it does come from petroleum extraction, and if you're not extracting petroleum from the ground, you're not getting NGL -- dry up one source, and you're drying up the other.
That leaves natural gas, and I'd have to do some conversion to sort out what fraction of plastics production is represented by the billion cubic feet or so of gas EIA mentions. And yes, other carbon feedstocks, including ag waste or captured / segragated carbon could conceivably feed plastics.
