What is this plastic chip packing material called?
I would Like to answer your question with an alternative image which would solve your problem.



These are called IC tubes/ Anti-static tubes for Dual In-line Package (DIP) ICs.
This is actually the handy alternative for shipment or storage of DIP ICs without causing damage to pins such as bending or breaking. You can find it on amazon or some other e-commercial sites in your country depending on their availability. Here's the one link from amazon
https://www.amazon.com/MULTICOMP-030-0012-TUBE-0-6-280MM/dp/B011O94IEE#feature-bullets-btf

I used these in my labs. We had the bulk of OPAMP (741), 555 timer ICs for many participants in a workshop. These tubes were very handy to deal with.