Lin Clark's talk makes this sound like they implemented a scheduler in React -- basically JS is single-threaded, so they're implementing their own primitives and a scheduler for executing those on that main thread. Sounds neat, but it also seems like an explosion in complexity -- perhaps there will be a bunch of weird scheduler bugs the operating system folks more or less figured out a long time ago?
That said, the early feedback from others in the React community is that the Fiber implementation is simpler overall and easier to work with than the "React Stack" implementation. Fiber is also explicitly built to support additional renderers on top of the core reconciler, while building renderers on the Stack implementation apparently required some levels of monkey-patching or reaching into internals.