Pentacene is synthesized from benzene, and the primary source for benzene is currently petroleum. It doesn't have to be, but benzene has always been a relatively cheap "garbage" byproduct of other products (first coke, then petroleum fuels). It is unlikely that over the long term extraction of fossil fuels would be a cost-efficient means of deriving chemicals that are now heavily subsidized by the primary products; bacterial synthesis would probably much more practical. That is to say one shouldn't dismiss non-fuel petrochemicals simply because the current cheapest source is petroleum -- it won't always be unless the demand for petrochemical fuels (or coal/coke) remains high. Ironically, then, things that are now petrochemicals could spell the end of the petrochemical industry if they contribute to a reduction in demand for fuel.

The author likely translated organic polymer to organic plastic, because they didn't realize that these words have very precise meanings and they thought that the word polymer would be 'scary'.

By "organic" they most likely mean carbon based, which leads me to believe that it is most likely petroleum based.