To answer the question "why this design vs. other nuclear rockets?" it comes down to operating temperature. Previous nuclear-thermal rocket designs, like NERVA, were designed with solid nuclear fuel in mind - similar to most nuclear reactors. On the relative scale of rocketry, that's a pretty simple design. ("Simple" != "Easy") However, this means your thrust is a bit limited by the melting point of the nuclear fuel assembly - the hydrogen (or whatever propellant) is being relied upon to keep the nuclear core from (literally) melting down. So: the propellant can only be heated to, say, 2500K before it hits the nozzle.
But if your design
assumes that the nuclear fuel is already liquified by its own prodigious heat, then the propellant can be heated much higher.
Earlier work by NASA and AIAA talks about getting up to 5500K. But, it seriously complicates the engine design, because now your design needs to handle molten nuclear fuel, usually at high pressure (to ensure it doesn't boil off), and separate it from the propellant (so you don't spew U235 out the back end). So we have this centrifuge design.