(Having not read the article), most likely because the cancer cells (at least at more advanced stages) are busy trying to replicate as fast as possible, so they take up nutrients at a much faster rate than non-cancerous cells. As to why Iron in particular, it is used as a cofactor for enzyme and if Iron is a limiting factor for replication then supplying it will lead to a burst of growth which then (presumably by applying strong oscillatory magnetic fields) you can target those cells directly to locally boil them.

How do the iron nano materials get there? probably a combination of vasculature and diffusion.

They have done this kind of stuff before with gold nanoparticles, iron is a lot more abundant.