Spark gap radio?

You can get into arguments about specifics by saying they still have light so they still have say EM radiation. But, what is and is not magnetism get's a little wonky when you get into the specifics. Strong, weak, electromagnetic force, and gravity. That's it. Without magnetism you don't get atoms.

However, if you hand wave that the induction coil is a transformer used to step up voltage and transformers work fairly directly though magnetism.

And plasma tweeters!