It's unusual that they specified "synthetic plastics". Natural plastics, in the sense of thermoplastic or thermosetting organic polymers, include birch tar, pine rosin, natural latex rubber (sometimes vulcanized with morning-glory juice), beeswax, and the shellac mentioned in the article. A mixture of pine rosin and beeswax known as "sealing wax" played an important part in 19th-century information security and high-vacuum apparatus. And of course pine rosin played such a crucial role in naval power during the 18th and 19th centuries that the first federal product-purity law in the US was enacted to prevent fake rosin and turpentine from being sold; the current version of the law is https://www.ecfr.gov/current/title-7/subtitle-B/chapter-I/su....

Cellophane/rayon/viscose is kind of a borderline case. The content of the finished polymer article is 100% natural cellulose, without even so much as a nitrate or acetate group affixed. But the process of dissolving that cellulose from plant matter so that you can form it into sheets or spin it into microfibers involves chemicals that are so nasty that nowadays they are used almost only for this purpose.

In my childhood (the 01990s, not the 01890s) ping-pong balls were still made of explosive celluloid. My father, who attended a mining college, demonstrated by dropping one onto an electric stove burner, not hot enough to glow visibly. It disappeared in a puff of flame. I was disappointed to discover recently that this is no longer the case for the ping-pong balls I found.