Neodymium is just the example that affects magnets and is easy to talk about, the Chinese clampdown is across loads of rare earths, and like neodymium they've cornered the market over a period of time by undercutting, stuff that has more esoteric uses that making magnets out of. I don't know if the clampdown includes export of products containing rare earths, that would make a sort of economic sense as suddenly you could only buy technological products from China, and it would keep everywhere else struggling to produce technology competitively.
When I say 'stopping of supply' I don't mean China's is totally stopping supplying the world, I mean people using the stuff suddenly have their supply stopped, because demand is elsewhere, in the scheme of things, 40 year obsolete technology used only for indulgence is not a priority use.