hmm looks like in a dielectric, EM waves only interact with the electron shells of atoms, and the restoring force for those comes from whatever quantum effect binds them to the nuclei[1].
Meanwhile in case of Alfven waves, according to the wikipedia page you linked, it's the magnetic field line tension that provides the restoring force...
Intuitively it feels right that such a force would exist, but I'm curious why.
[1]: https://www.feynmanlectures.caltech.edu/I_31.html