>Is there some sort of relativistic mass-energy equivalence stuff going on

indeed. the surface magnetic fields of magnetars are measured in tens of giga-Teslas. this results in an enormous energy density, which greatly exceeds regular matter, even with its large rest mass term.

edit: some quick napkin math reveals an energy density on the order of hundreds of yotta-joules per meter cubed. aka millions of billions of gigajoules per cubic meter.

IIRC some of the most extreme magnetars produce fields that are higher density than solid materials.