In many post-apocalyptic works of fiction it's a disease that wipes out much of humanity; what if instead it was a bacteria or pest that rapidly consumes all our plastic that causes civilization to collapse?
Also you always have fluoropolymers to fall back on partially.
If they're right about the enzyme then the threat is possible. It's different from organisms that eat wood because we are pretty good at mass producing stuff.
A bacteria making an enzyme that allows it to gain nutrition from plastic would certainly be an interesting problem for humanity. I cannot say if it would be doomsday level or a minor inconvenience, but neither can easily be disregarded because there is no precedent.
Wood is not a good example because nature has had nearly a billion years to figure out an efficient way to reclaim the energy in wood and the closest it got is slow fungal process. This is why when we make wood structures we paint them or treat the wood with fungicides.